I don't think either one of you are right, nor are either of you wrong.
It really depends how hard someone is on their bike that determines if someone should pitch the single wall rims or keep them and fix them.
For some people, a single wall rim is adequate. It will hold up, and not need trued that often. For others, it would need trued a lot, and possibly even warp the rim itself.
For the first person, dishing out $100+ for 2 decent rims wouldn't be that ideal. From our perspective it might be just because most of us see single wall rims as crap, but for someone who isn't that hard on them, it really wouldn't.
Now for the second person, dishing the same amount out would be ideal. Let's say for the sake of ease that a shop would charge $30 total for truing both wheels, and said person needs their wheels trued a few times a year because of how hard they are on their rim. Once they go to get their wheel trued for a 4th time, they could have just as easily bought double wall rims and been done with it. Of course double wall rims need trued as well obviously, but not as much as a single wall rim would need.
That's not counting if the person knows how to true rims themselves though. Even then if you do and you're truing your single wall rims every other week, you're gonna get tired of doing that pretty quick. Someone who knows how to true wheels, isn't that hard on them, and has single wall rims, probably wouldn't mind doing it once, maybe twice, a year.
I have double wall rims and know how to true them. Front gets trued probably twice a year, maybe 3 times, but the back gets trued quite often because I'm hard on it, and land funny on my back wheel sometimes. I'd get so pissed if it was a single wall and I was doing that all the damn time or wasting money having someone else do it.
TL;DR- horny unicorn found in Uganda impregnates bike shop employee while truing single wall rims (With sexy results)