I'm placing my hand over a Bible right now because I know you're not going to believe this, but I once charged a $51,000 Lincoln Navigator.
I used to work as an assistant to an extremely wealthy individual, and he asked me to go pick up the vehicle for him (he had negotiated the purchase with the dealership over the phone - he bought cars like packs of gum...the Navigator became his "beater").
I had several of his credit cards because I was always buying things for him. He told me that, for a reason I can't recall, he needed the vehicle ASAP and he wasn't around at the moment. So I went to the dealership and put the thing on an Amex. The dealer was hesitant but only because he had never made such a transaction before. The card's limit was astronomical, so that wasn't a problem. The dealer and I both spent a little time on the phone with the CC, and the situation was resolved in well under an hour.
When I saw my boss the next day, he wrote a check for the full amount and it was paid off within 72 hours.
This happened in 2000 in the Chicago area. Maybe the dealership screwed themselves out of 3% (almost $1700) or maybe they didn't. I don't know. All I know is that the whole process was quick and relatively painless. The Amex I used was not a miles- or reward-bearing card. I'm not sure if that made any difference (I doubt it).
I suspect that this is an exception rather than the rule, but the point is at the very least it pays to ask.