I am just repeating what he said. Rubio said he paid the credit card directly for the charges.
Or, he could have gotten reimbursed for business expenses and paid the whole thing off from his account.
There are a variety of ways this would be 'kosher' and I can't see why Rs are making a big deal about this. It is not necessarily unethical.
I could use my corp card for "personal" expenses if need be, but I'd rather get the rewards points on my personal account(s). R's who are making a big deal about this just really don't understand the different ways things work.