Fenders may have caused worse problems in that situation. You have a whole lot going on on a frame without a whole lot of clearance. It wouldn't take too much to have gummed up the works enough so that the bike wouldn't have moved. That's generally been my problem with fenders, especially with off-road riding. It doesn't take a lot to go from riding in the wet to walking in mud.

Generally speaking, I'm not a fan of fenders. They rattle, they rub, they get gummed up with gunk, they make putting the bike on top of the car difficult, they make putting the bike inside the car difficult, and, honestly, they provide only minimal protection. If I'm riding in the rain, I'm usually riding in a rainsuit which protects me more than the fenders do.