Not sure why this would matter. You know that implication is directional, not symmetric, right?
To be more explicit: Given that for-profits can be given tax-breaks for (hopefully) good reasons, what would be the reason to give non-profits tax-breaks, if not for altruism? After all, as you point out yourself, you can get tax-breaks also as a for-profit, so you don't need non-profits just for that reason.
* Given that for-profits can be given tax-breaks for (hopefully) good reasons [which are not altruistic];
* therefore non-profits can be given tax-breaks for (hopefully) good reasons [which are not altruistic].
A defense contractor designing missile guidance qualifies for the Exempt Purpose of "scientific."
A megachurch with a private jet qualifies under its "religious" category.
These do not specifically require altruistic intent. Congress chose to subsidize certain categories of activity (religious, scientific, educational, and so on) because it wanted more of that activity produced, regardless of the motives of the people doing it.
I’ll ask my mother if I was dropped on the head as a child.
Oh, I am sorry if that was the case. I amended my answer to be more explicit, as I already anticipated that you are not into logic.