Wrong. If the government razes your house, takes your bank account, imprisons you, and then realizes its all a mistake and says, "Sorry" but refuses to make you whole again (and then some), are you telling me they shouldn't be responsible for your attorney's fees when you sue and win?
Let's not let our hatred of the ACLU (which is entirely justified) ruin our perspective here. The poster you responded to was 100% right; they shouldn't be winning these cases, but in the example above you should. If this law wasn't in place, you'd never be able to find an attorney to take your case, and you wouldn't win on your own.
The headline is terribly misleading. This statute is called a "fee-shifting" statute. It isn't public financing of anything, and there are other fee-shifting statutes to apply to other litigation. In this case, the government just happens to be the defendant, and the government just happens to be taxpayer financed. But that doesn't mean the fee shifts become public financing.
Under the aegis of its Foundation, the ACLU could get away with murder. Within that structure all kinds of financial misdeeds can be hidden. For example, the ACLU also receives private funds. It would be interesting to know what kind of financial activities officers of publicly-traded corporations engaged in and whether their donations to the ACLU were properly accounted for on company financial statements, whether shareholders were duly notified of corporate ACLU donations, whether the donations were made from corporate funds in the names of private individuals, and whether the ACLU itself properly accounted for these donations when filing official statements.