I think the argument is that players on teams in high tax jurisdictions (such as Toronto) have to spend more on high-end players (let's take John Tavares at his $11m cap hit for example), which gives them less cap space to construct a team, whereas an equivalent contract for John Tavares if he signed for a team where there's no state tax that results in the same net pay would be... well, less than $11m in gross compensation certainly, I'm not going to try to do the math on it, but it does leave the team with slightly more cap space.
While a player could hypothetically earn more money from endorsements (and the like) on top of his salary by signing with Toronto, I've heard of no such case where a player agreed to take, say, a $9m contract in Toronto (as opposed to say $10m in Nashville) because the negotiation of that salary was "well you can end up making more money overall by signing here so we can get away with giving you a smaller contract" or something like that.
I can buy that argument as being valid, but I'll admit I don't have an informed opinion on whether I agree or disagree with it. I'd have to see all the numbers on it to form a truly informed opinion, and because players' tax returns are not public information, that's not possible.