Yep, inflation is just another kind of tax, and one that's quite hard to avoid.
Market forces like inflation aren't a person exerting control over them. They're the results of humans acting within social structures. These people have control over social structures; they're the elite. They can counter that market force with some other market force. Taxes? That's cold, hard math. There's no way around it, no feeling of agency to be had. So while it might be harder to avoid, it's not the financial effect that they worry about, because they have enough money to weather that. It's the feeling of obligation and powerlessness in the face of others that they can't brook.