This is quite different than a bailout. They can’t just go to their customers and say, hey, we got this bill now you have to pay for it. They can raise fees, but then customers can go to another bank. They can lower what they pay in interest rates, but again, customers can go to other banks. Or customers can buy treasuries instead of keeping money in bank accounts. Banks are not the only place to keep money, nor the only way to raise money. Sure, chances are that some of the money will come from raising rates on customers, but some of this will just come out of bank profits.
So by your own words, it’s still a bailout being paid by taxpayers.
It’s just that taxpayers may decide to pay in either money (fees, less interest) or time (switching banks and updating payment methods, or taking money out to buy bonds).
In a painfully literal sense, yeah it's being paid by tax payers because everyone pays taxes. The better distinction is that it is not paid via tax revenue. Even if the FDIC has to levy fees on banks to help cover the cost and the banks raise fees on their customers to cover this, this is not the same as the tax payers funding the bailout because they're not funding it in their capacity as tax payers (where they have no option but to pay the government and would probably prefer their money go towards building a school or something). Additionally, the banks wouldn't just be scooping the extra money out of people's accounts, it would be in the form of higher fees or something which the customer could decide to leave the bank over if they desired. Most wouldn't do this, but again the point is that there is at least an option where as a tax payer funded bailout there isn't. At a certain point, everything in the economy is connected and you could drill deep enough to say the tax payer pays for literally everything, but at that point the label becomes meaningless.
