According to the USBC website, no mention of any 'stabilizer' thumb use.
Holes or indentations for gripping purposes shall not exceed five and shall be limited to one for each finger and one for the thumb, all for the same hand. The player is not required to use all finger holes in any specific delivery, but they must be able to demonstrate, with the same hand, that each gripping hole can be simultaneously used for gripping purposes. Any thumb hole that is not used for gripping purposes during the delivery would be classified as a balance hole.