I think "guy buys" is a holdover from the "guy does all the inviting" days. Because it is accepted that the person who issues the invitation pays, and it used to be unheard of for a female to initiate a date. Does Sara come from a really traditional background where those old rules haven't been completely set aside?
However, from what little I know about online dating (I've never done it but some of my friends have), it's generally advised that for a first-time meeting, you (a) meet in a public place, (b) have your own transportation and (c) go Dutch. That way, if your date turns out to be Creepy McCreeperson, you're not into him/her for anything. (Because some McCreepersons will insist that you "owe" them a kiss, or more, if they treated you -- even to coffee.) Sara was foolish on at least two out of three counts.
A good rule of thumb for any date, first or 51st, met online or IRL, is if someone wants to change the plans and it's going to cost money, the plan-changer picks up the tab. I've been in situations where my plans with someone didn't include dinner, but I'd worked through lunch and was starving. I bought my own food and always offered to treat my companion and/or share.