I sort of agree, but also, especially under exam conditions, arriving at the (correct) answer I would definitely think 'well obviously I went wrong somewhere'.

Yeah, but the fact that it's a little tricky to think about, and that the trickiness doesn't come from the algebra part of the problem are exactly why I would say that's a terrible question to ask under exam conditions in the first place. I'd be totally cool with assigning it as homework, both because it could generate some meaningful discussion, and because doing the problem on one's own and with ample time to think gives the student the opportunity to work through the "paradoxical" aspects themselves.