Variations must be consistent in fulfillment channel???

A catalog team rep is telling me that the fulfillment channel on child variations must be consistent. In other words, you can’t have a variation setup that has some that are FBA and some that are FBM. It must be either, but not both. This rings as being completely made up. I’ve requested the rep to show me where that is documented, and she hasn’t been able to provide it. Has anyone else heard this?
More details, I recently merged existing listings into a itempackagequantitycolor variation. All of them work and display correctly except one. This ASIN shows as part of the variation on the inventory screen but still displays as a stand-alone listing on the Amazon storefront. After receiving the normal BS responses from seller support reps, I finally called and got to the catalog team. The rep doesn’t have a clue, and I think she’s just making stuff up to get off the phone.