This is actually horrible advice. Non profit clubs that rent ice are at a distinct disadvantage. They don’t control the ice and pay premium for all rentals. You’re going to get less for your money because there’s an expensive associated with every ice touch. Rink owned clubs can offer more ice, better slots for less money per touch. Again, this isn’t saying the tuition is more or less but your price per ice touch will be more at a non profit club. You end up sharing more ice than less.
Btw - these friendly not for profit clubs still pay board members, president, director etc. Nothing is free.
I don't think that you can paint all non-profits with the same brush. In my area, there are some very high functioning non profits, and there are some that are run like a hot dog stand. What it really comes down to is who the board members are, how much time they have to donate, and how passionate they are to learn and implement "best practices" into the organization.
What gets lost in a lot of this is what the organization prioritizes; is it winning or development? It's very tricky to deliver both alot of the time. Winning is a byproduct of development; not so true the other was around.
FWIW, I was on the board at our local non-profit and as the treasurer, I can confirm there weren't any non-coaching salary expenses. So that is not true for every non-profit either.
Where you can draw a line of distinction between profit and non-profit, is that the non-profit is simply looking to break even so that plays as an important factor in the final tuition. As another poster pointed out, prioritize good coaching for your child's age bracket and quality of organization second.