I don't think there was anything serious that didn't get reported. We never had to use anything beyond a single band-aid for non-recordable injuries that I know of and unless you want the office staff reporting every paper cut to OSHA, I don't think they were being unreasonable there.

If anything I'd worry more about the temperature of the floor or the number of hours worked, but it's hard when some people had second jobs or what have you.