Syag, “someone else’s expense” (aka OPM, other people’s money) means in this case accepting non-Jewish government, or even Jewish, charity funds designated for poor. Accepting community funds for learning, teaching, being a Rabbi is less problematic.
Many people avoided taking. Chafetz Chaim, for example, had a store and sold his own books, personally verifying that printing is correct and travelling to sell them. When and if accepting OPM, feeling responsibility of that.
Now, you can do proper heshbonos and take money responsibly, of course. And I do not doubt that many in Kollel do. R Salanter did not hold by pas isroel when travelling to a resort to restore his health, because someone donated him funds to eat healthy, not keep his humros. As R Dessler explains, world most fundamental difference is between givers and takers. But, you can give as a taker (grudgingly), and you can take as a giver, with appreciation, responsibly, etc.
So, when Meir is suggesting that $1800 for a poor person is not much as it barely sends one kid away, you can see that he is not taking all scholarship about the issue seriously. The irony of dedicating yourself to learning while disregarding the percepts you are learning is breathtaking.
When such a kid learns a gemora that father is obligated to teach a child a craft so that he will not become a gazlan – does he ask a father? what is the tirutz? genuine question – did anyone’s kid ask that?