I’d like to be able to flip a coin to determine whether or not I have to pay a bill, but I don’t think that’s what my student meant here.
Nor do I think she was imagining a taxpayer turning a bill face-down (or face-up) on the “pay” pile. Of course maybe she was thinking about how bills were received at her house: Maybe her father flipped when he saw how high they were.
What we have here is ignorance of a figure of speech, “foot the bill.”
Now, figures of speech work because they create tiny pictures in the reader’s (or hearer’s) mind, and those tiny pictures convey meaning more vividly or immediately or charmingly or at least clearly than more mundane terms could. For instance, “You can talk yourself blue in the face before I pay any attention to you” may be longer than “Don’t waste your efforts trying to convince me,” but it is also stronger.
Sometimes, though, because language reflects its culture, the little pictures become inaccessible when the culture changes. Then we try to create pictures that make sense in our own context—and may or may not be right. A simple but useful example of this situation can be seen in the recurring analyses of the term “brand new.” Everybody uses the phrase, but most people are nonplussed if asked where it comes from. Was it always “brand,” evoking cattle, or “brand,” evoking something else, … or “bran,” an intriguing, but most likely only folk, etymology based on a notion of early packing noodles? (You can see a recent foray into “brand new” here.)
And as with Mondegreens and other creative errors, if the hearer has no access to the image on which the figure of speech depends, she will “hear” a word that makes more sense to her—or, in the case of my student here, a word that makes no less sense to her.
So for her, “foot the bill” becomes “flip the bill.”
The OED (print version) devotes FIVE PAGES to meanings of “foot.” Most of these are for “foot” as a noun. When we come to “foot” as a verb, we must travel through “dance,” “walk or step,” “traverse,” “establish or settle,” “kick or threaten to kick,” “tread or crush with the feet,” “use the feet in kicking,” “seize with talons, as a bird of prey,” “follow the tracks of, trace,” “make or attach a foot to,” “end with a postscript, as a letter,” AND THEN, “add up and set the sum at the foot of a bill” and “settle or pay a bill.” There are three more verb meanings or usages after that.
I have to admit that my little mental picture was for none of the above; it was, instead, a variant of “endorse”: I imagined that some people could co-sign a loan or approve a contract by signing it on the back (endorse), but that more commonly people did those things by adding their names at the bottom, the foot. By this picture, I would have made the taxpayer the default payer, so that if the government, or whoever, failed to settle up, the taxpayer would have to step forward (on, presumably, his or her feet!) and pay. But I was wrong, although not as wrong as if I had imagined some kind of acrobatic flipping going on.
By etymology, and by reason, when the taxpayer foots the bill, the taxpayer pays the bill: no middle-person involved. And that’s certainly true, since the government’s money is taxes, and so whenever the government spends money the actual spender is the conscientious taxpayer, loyally sending in every Ides of April his or her little investment in the well-being of the country. (For the purposes of etymological discussion I am ignoring investments from other nations here, so don’t mention China to me!)
Alas, many politicians are now suggesting that the taxpayer should be allowed to flip off the bill, especially the wealthy taxpayer. (Urban Dictionary will give you the meaning of this modern phrase, if you are in any doubt; I invite you to find your own way over to Wikipedia for more than you want to know about “the finger”…) My student’s question would suggest that she does NOT have this activity in mind, but does have an attitude that would be hospitable to it.
Our society seems to change at a perpetually accelerating rate. Use your own favorite figures of speech while they can still communicate to someone else. Maybe that’s the chief attraction of “retirement communities”: being of the same generation, everybody speaks the same language.