OK. Let's give it another shot.

Note that I have no axe to grind here; I'm trying to give an explanation, and feeling like that explanation is hitting some filter that makes it get treated like noise. (I can understand tuning out politics or philosophy; I generally try to as well, especially the former. But this is a fundamentally political/ethical question, and it can't be evaluated in isolation in pure economic terms. Or, at least, choosing to ignore everything but the pure economic terms is itself a political/ethical position.)

Forget, for a moment, the number at the bottom of the balance sheet at the end of the day. While I'm a fan of consequentialism (which it seems like you're using as the motivation for asking about equivalence), I consider misleading argumentative tactics to get there unethical in and of themselves. People should be very careful using rhetoric or deception even to enact positive change or produce net-positive consequences. And it's safe to say that the change advocated for here is at the very least not unambiguously positive.

But in any case, the number at the bottom of the balance sheet isn't the only one that matters here.

There's a certain tendency to privilege the status quo, both for invalid reasons (sunk costs fallacy, etc) and legitimate reasons (change has a cost to implement, and frequent change can cause inefficiency). So, as an argumentative tactic, it may be in the best interests of someone attempting to make a change to make it seem like the status quo already, and perhaps instead argue that there's some special circumstance or loophole that's being closed.

Ask people how they feel about raising taxes. Then ask people how they feel about the government spending less money. Even though both change the bottom line of the government budget in the same direction, the former will elicit far more negative responses, and the latter will elicit far more positive responses. And that's not just cognitive bias talking, either (though that likely plays a part too); there's a legitimate semantic difference there. Raising taxes means the government is claiming domain over more resources. Spending less means the government is taking funds it already stakes a claim over and spending less of them. The former makes the government larger (in that it controls more money and passes more money through its budget), while the latter makes the government smaller (in that it controls less money and passes less money through its budget). This obviously intersects with politics (large/small government, and the role of government in general), but even without that, there exists a semantic difference between deleting an expense and collecting a tax.

Let's stop there for a moment; does that semantic difference make sense, without further complication?

Now, as an added complication in this case, we're talking about non-profit organizations, so there's a second semantic quibble there. However, it's not as if non-profit organizations pay tax and then get it all back as a subsidy. They pay 0% tax to begin with. So, again, in terms of government budget size, the hypothetical taxes that would be paid by a non-profit if they were not a non-profit are not part of the bottom line. That then directly gets into the positioning by the article. The amount given to taxpayer-funded universities consists of actual tax funds, collected from taxpayers, included in the government budget, and paid out to universities. The amount of hypothetical tax revenue that would be collected from a non-profit if they were not a non-profit, on the other hand, was never collected in the first place, is not part of the government budget, and does not contribute to the size and purview of the government.

In terms of the number you can look at to see the difference, look at total government revenue and expenses. (Which, I would argue, should be equal, but that's a separate issue.) Either raising revenue or lowering expenses by a given amount has the same effect on the bottom line, but they have different effects on the nature, size, and purview of government.