In a codeshare dispute, both airlines will blame each other, but it is important to focus all your efforts on the ticket seller.
The emphasis on the contracted airline seems like is helping United by diverting blame away from its brand. Legally United might be able to dodge a few issues based on it and technically they might be in the right over what they did. Morally and as far as public perception goes, they should bare full responsibility.
Nearly every major airline in the world that serves feeder routes does this.
Remember that Republic also does the American Eagle flights.
If these contracting arrangements weren't possible, then you'd see many major airlines dropping the routes.
The typical plane for the route in question holds 76 passengers. With margins around 1% or less, that flight is making a tiny profit. Let's say, just for the sake of argument that the average ticket price was $200. That's $15200 in revenue for the plane (excluding cargo.) That airplane typically has two flight attendants, two pilots and an assortment of ground crew. Also remember that close to 50% of ticket revenues are actually taxes and fees that don't go to the airline but to government. So that $15k is now closer to $9k -- that's revenue, not profit. This if for a nearly 1 hour flight.
Do you know the operating costs of your average Embraer 175? Landing fees? Gate slot fees?
My point is that United/American definitely don't want to pay higher union wages for routes that are operating on razor thin margins as it is. If they raise ticket prices, planes will be less full, crushing the margins even more, if they pay more, that also crushes the margins. Either way, even a slight increase in costs somewhere in the system destroys the profitability of the route.
Perhaps we should be complaining about government taking such a huge proportion of taxes and fees rather than United trying to minimize costs. For a business making literally 1% margins on most flights, we certainly have a lot of opinions about how bad they are when they try to keep costs down.