Are MHC Proteins the Most Polymorphic Human Proteins Known?
Yes.  There are many MHC (MHC in humans is called HLA) genes.  The classical loci — Class I A, B, and C, and Class II DP, DQ, and DR — are the most polymorphic.

Here's a table from a 2002 article which clearly shows the number of polymorphisms.  It's no contest.



It's worth me pointing out that those numbers are wildly out of date.  The IPD-IMGT/HLA can provide full lists of known HLA alleles, but the exact numbers are in the tens of thousands:







The person you spoke with was probably referring to sequences called microsatellites.  These are small regions that are polymorphic and quite variable between individuals, and using a number of these together can be useful for genetic fingerprinting, but each individual microsatellite will not be as polymorphic as HLA class I A, for example.