Bad understanding of the rules in this thread leads to poor advice.

While the carrier sets the carry-on allowance, it must file that with the FAA. It then becomes an FAA rules violation for the carrier to fail to enforce the allowance it has set.

So, unless you want to play junior lawyer, that is routinely condensed to "it's an FAA violation for which we (I) may be fined....) That is neither a lie nor inappropriate. It's not a court argument but a boarding gate.

If the GA was concerned, it was likely because he had been warned that there was an FAA inspector around. While there is no requirement that each passenger personally handle their own carry-on, having one person head down the jetway with four bags, is a good way ---- if there is an Inspector ---- to have the boarding stopped and the situation dealt with.

If your wife required assistance, it was fair to ask the carrier for that and it would have been obligated to provide that.