Perhaps forensic magic is better than you're assuming it is. There may be ways to tell how much magic has been used in an area, and on what. I've seen fanfics at least with ways to check what spells were most recently cast by wands. It would be pretty obvious that the Potters never got a chance to fire a spell off.
That spell is canon. In the fourth book, HP & the Goblet of Fire, they use the Priori Icantato spell to try and determine who cast the Dark Mark. There's also legilimens, the spell used to look into another's mind. Using just these two spells, you can set up a reasonable course of events.
Presumably, forensics arrives on the scene and sees the destruction. There's a set of Voldemort's robes on the ground along with his wand (NB: you never ever part with your wand). There's a dead Lily and James Potter, along with a baby with an odd looking scar. F...
(And somewhere in the back of his mind was a small, small note of confusion, a sense of something wrong about that story; and it should have been a part of Harry's art to notice that tiny note, but he was distracted. For it is a sad rule that whenever you are most in need of your art as a rationalist, that is when you are most likely to forget it.)
Why does the wizarding world believe Voldemort used the Killing Curse on Harry? Whether or not the Love Shield exists in MoR, I doubt most wizards had an >epsilon prior for the Killing Curse resulting in a scarred but otherwise unharmed target, a dead and burned spellcaster, and a destroyed building. There were no surviving witnesses except Baby Harry. Where did that version of events come from?
If I was Joe Random Wizard and heard that evidence without names attached, I would naively hypothesize: Dark Wizard shows up at house, encounters mother + father + their allies. Battle ensues. Parents and Dark Wizard are slain. House is destroyed and baby is hit by debris. There is one obvious question - why the allies didn't take the baby with them - but any answer to that is more plausible than "There were no allies; the most reliable curse in the world backfired on its most experienced practitioner."
Not that the "reflected curse" story was hard to sell. People are great at not asking the next question when they want to believe.
We have some additional information about the events of that evening:
What really happened at Godric's Hollow?
PS. If the Love Shield does exist in MoR, do you suppose Bellatrix could cast it?