Best guess that:
1. the employee presented false documents. This is common in CA and elsewhere; most illegals actually purchase very convincing work papers and ID. There is currently no way to do a even a simply check on validity.
2. The employer strong believes the injuries are bogus. Looks like it from the description of them.
Keep in mind also that illegals rarely contribute to employer provided health insurance. They use work-comp as a makeshift "free" healthcare system for non-work ailments.
ICE doesn't seem to have trouble spotting forged documents. Maybe they could give employers some tips. Trouble is employers don't want any tips as long as they get cheap labor and increase their bottom line.