They do have to pay for it, even if it’s a government charter. The government has a floor full of accountants that figure up the bills. I think, I’m pretty sure this is true. Even the president gets billed for non-official meals, if I’m not mistaken.
Regardless, they are only pissed at the prestige lost in not traveling with POTUS. I don’t care if they pay or not. There is still nothing in our Constitution that says that they have that right over any other citizen.