Who doesn’t want to save money when they can?
I think what they're saying is, in the context of towing, a few pounds of tire savings will not be worth the cost of new tires, assuming your current ones are still good. There are other things you can do to save much more money while towing than switching to slightly lighter tires.
However, if you're about to purchase new tires anyway, weight is a valid consideration because it will incrementally save you gas/gain you performance and wear/tear continuously throughout their life, and it may be worth it provided you aren't giving up anything important to you in selecting the lighter tire size, such as load capacity, speed rating, or wear and puncture resistance. I know I considered tire weight when shopping for my next set.