In my recent ( last 24 months) dealings with LACNIC, they were very thorough in validating information and enforcing documentation requirements as we needed to modify some things after some corporate changes. Obviously that may not be representative of all their operations, but they were quite on the ball in making sure we (still) were who we said we were.
I think it's a tricky argument to say what LACNIC *should* or *should not* have done. We don't know all the facts. But we all know that fraudulent business records are used all over the world for things like this all the time. Calling for a complete audit of LACNIC feels quite extreme absent a pattern of issues, which doesn't seem to have been presented.