I can't believe there's still an argument over who determines the number of carry-ons allowed. A quick Google search turned up 14 CFR 121.589, which states that an airline may not allow carry-on luggage unless they have an approved "carry-on baggage program".

On October 8, 2001, as was stated previously, the FAA made the requirement that air carriers limit carry-ons to one bag plus one personal item.

It appears that most of Title 14 of the CFR stayed with the FAA and was not transferred to the TSA (at least as near as I can tell). The TSA administers rules found in Title 49 of the CFR.

Therefore, it is not an airline policy nor a TSA rule. It's an FAA rule.