Glad you were not seriously hurt. Because we enjoy riding out bikes, we sometimes forget they are fairly complex machines, with lots of ways to go wrong.
Fred DeLong, in his '70's classic on bikes, did not underestimate how many things can go wrong on a bike. He included in his book a "checklist" for inspecting a bike that covered several pages. It was a checklist that he felt owners should work through on a regular basis. He had a shorter checklist for a daily bike inspection.
If you put a 37mm tire on a rim that was designed for 25mm tires or 28mm tires, that could put extra stress on the rims. If the bike was designed for 23mm tires and 25mm tires, as many current road bikes are, using 37mm tires would greatly reduce the clearance between the fork and the front tire and between the rear tire and the chainstays. If a rock, or other road debris wedges between the fork and tire, or chainstay and tire, something is going to fail. If the "wedge" is against a carbon fork, that fork may fail. If the "wedge" is against a sturdy chainstay, the rim may give way and fail.
We assume that the bike manufacturers are making unbreakable equipment. THEY are assuming that we carefully read owner's manuals and read the warnings that manufacturer's post on their websites. We are probably over-estimating them, and they are probably over-estimating us.