get a 2nd opinion...

Yes, and have that company be one that offers vinyl plank flooring that looks like wood. I understand that it is looking better these days. Some of the early stuff tended to look greasy over time, but that may have had to do with waxes or polish the nursing homes I saw them in were using with their floor cleaning machines.

I have Forbo Marmoleum sheet flooring and it seems to do really well with my uneven floors. The installer first made templates of the floor areas with luan, then glued the Marmoleum to the luan, then, after making certain they fit together, glued the luan/marmoleum pieces to the floor. Doing it that way, it took care of any fitting problems due to dips or high spots on the floor, they were just dealt with as they came. I imagine that vinyl plank flooring might be as forgiving.

I would not tell the new guy about the other fellow saying your floors were uneven. Let him tell you what you need to do, how much your hardwood will cost and ask if he foresees any problem with installation. If he says "no," then you might mention what the other guy said and about him looking at the joists in the basement. It will be interesting to hear what he says about that...