First, they didn't know what they were doing.

Yes, the vertical truing can be done. (This is assuming the rim is not bent and simply needs to be trued.)

Unless the rim is trashed (since you have ridden on it I am going to assume it is NOT trashed) you do not need to buy new rims. No, the stock rims are not as good as spendy new hand made rims but that does not mean need to replace them. At some point you may want to but that is not now.
If you are a big fella you may start popping spokes. (I'm 280 and have never popped a spoke on the original rims that came on my Trek hybrid.) At that point you may want to think about talking to another LBS about rebuilding the rims or think about some new rims. The only time you must buy a new rim is if it is actually cracked/broken or bent beyond repair--not the case with yours.

In conclusion, you don't have a rim problem, you have a bike store problem.