That is very true, however I believe that they enter into cobranding agreements to encourage business. I find it difficult for me to reward activity that I don't like. You could say it is voting with my dollar.
The low credit is puzzling and is either a mistake, policy for the card or because some odd ball thing like x credit cards closed and x opened recently. My platinum card regularly has large charges that are always paid in time. That may actually be the problem, since it doesn't take but a couple of days to get a reimbursement check, I often pay it back with in a week of the charge.
Not real thrilled with the Hilton I'm in now, but that is a different forum.