MacGyver/WMG

MacGyver was Jesus Christ.

 * In the second season episode "silent World," MacGyver is heavily involved in a voice-guided missile project which incorporates technology that is also being applied in the creation of a device which allows the deaf to hear. The epilogue features several deaf children thanking MacGyver for letting them hear for the first time in their lives.
 * Also from the second season, "Pirates," in which MacGyver helps a crippled boy to walk... by retrieving sunken treasure which pays for the boy's surgery.
 * "Out in the Cold" finds MacGyver skiing, which is little more than bipedal movement over (frozen) water.
 * "Passages," from the fifth season, features the death of . MacGyver also goes into a coma, where he finds himself aboard Charon's Ferry (a cruise ship), about to cross the River Styx. Also there are and MacGyver's long-deceased parents. MacGyver doesn't cross, but instead is "resurrected" by waking up from his coma. (It should be noted that MacGyver works for the Phoenix Foundation.)

Murdoc is a Sword Immortal.
This is how he keeps coming Back from the Dead. Mac isn't going to cut off his head, so he's likely still out there.

MacGyver is a "good" counterpart of James Bond
Back in the 1950s, James Bond was selected as the ideal super soldier specimen to be cloned. However, as Metal Gear Solid has proven, only a genetically perfect clone can exhibit such radical differences. Observe: Unfortunately, MacGyver just wasn't good enough for British Intelligence; he was missing that essential bull-in-the-china-shop quality. So he was traded to the United States. The rest is history.
 * James Bond is a cool name. Angus MacGyver... isn't.
 * James Bond is sexy and dangerous. MacGyver is the type of boy that your father would set you up on a blind date with.
 * James Bond wears expensive designer suits. MacGyver wears a suede jacket with a polo shirt and blue jeans.
 * James Bond drives the coolest cars from Aston Martin, BMW, and Lotus. MacGyver drives a dingy old Jeep, which (to avoid risking coolness) is later replaced by an old station wagon.
 * James Bond is supplied high tech-gadgetry by Q Branch that run on nonsensoleum. MacGyver builds his own gadgets from mundane objects (although he also has a pocket Infinite Improbability Drive that he uses on them).
 * James Bond has no problem with killing people and legal permission to do it. MacGyver tries to avoid killing people; his villains die (when they die) by accident or by direct application of the Villain Ball. James Bond uses guns while MacGyver doesn't.
 * The number of women James Bond has chosen not to sleep with is exactly the same as the number of women that MacGyver has slept with (i.e. very few).
 * James Bond, in spite of never seeming to use any contraceptives, has never ended up with children from any of the women that he has slept with. MacGyver, however, manages to end up with one in spite of the very few women he has slept with and the fact that one would assume he would use contraceptives.
 * Even if MacGyver didn't have any contraceptives, he would probably be able to make one out of like, a rubber band and a condom or something.
 * Or maybe, just, you know, use the condom. Unless the rubber band is for extra added springyness, maybe?
 * Maybe the condom was a magnum and he needed an elastic waistband at the bottom? Because he couldn't "fill it out"?
 * James Bond has a bombastic, jazzy theme song. Macgyver has a little Casio ditty.
 * James Bond saves the world. MacGyver saves the kids of the community from counterfeit baseball cards.
 * James Bond spends Christmas saving the world from a bioterrorist threat. MacGyver spends Christmas helping a local gym run a charity play.
 * James Bond spends his free time in casinos, gambling with high stakes and scoring with plenty of beautiful women. MacGyver spends his free time going on nature hikes and doing social work with the community.
 * On the flip side, James Bond enjoys golf, a sport second only to shuffleboard amongst old retired men. MacGyver enjoys hockey, a sport second only to rugby for brutal violence outside the rules.
 * James Bond managed to kill his archnemesis eventually. MacGyver's unwillingness to kill anybody is so powerful, it selectively rewrites the laws of the universe to allow Murdoc to survive crumbling buildings, point blank explosions, thousand foot falls, and being submerged in boiling water.

MacGyver has three brothers; their names are Alton Brown, Adam Savage and Jamie Hyneman.
There is no better explanation.

MacGyver is a Spark
He can improvise complex devices out of any available material, and they always work even when physics says they shouldn't.

MacGyver is a near-immortal being who engenders the Starfleet Corps of Engineering.
In NextGeneration episode The Survivors, we learn that one Kevin Uxbridge is a Douwd: an immortal, Q-like race that specializes in hiding their identities. However, we have seen Kevin Uxbridge before: Harry Jackson, Mac's grandfather. Jackson cared for Mac after his "real" parents were killed; eventually they were estranged and later reunited. We know that the Douwd specialize in false identities AND that they can love humans. Since they are nearly omnipotent, it is conceivable that they would be able to foster children with humans. Therefore, we can postulate that Uxbridge, living on Earth, impregnates Mac's mother and then creates a "false father" in his own image (we have seen Uxbridge do something similar), possibly so that Mac will grow up with two human parents. After their deaths, Uxbridge regrets his decision and isolates himself from his progeny to protect Mac from finding out he's half-Douwd.

Mac's half-Douwd nature gives him long life and subconsciously powers his physics-defying prowess: either he bends physical law to conform to his needs, or creates useful items in proximity to himself when in danger. His constant manipulations of reality give rise to weird phenomena that span the universe, creating subspace and other Star Trek phenomena, as well as explaining all the physics-defying moments in the series. Uxbridge, who indulges often in denial on a massive scale (as we see in The Survivors), only eventually accepts that he is directly responsible for Mac's actions and, after a brief period of reunion to ensure Mac has developed in a sensible direction, fakes his own death so that he can relocate and start another new life.

The Starfleet Engineering connection is now obvious. That branch of Starfleet produces miracle workers on an absolutely unheard-of scale, with their own physics-defying aura and problem-solving ingenuity. The "main cast" engineers (all human or partially-human, mind you) must all either have studied at the feet of the master, or must be his descendants. Their own short-lived nature comes from the dilution of Douwd blood.
 * Transporter Chief O'Brien was also contemporaneous with Mac, but since the episode in which O'Brien and Mac interact featured time travel, it's likely this was just a time travel accident.