[eru]

There's also aircon at government buildings here where I live, that you can visit for free.

However it would still be a bit silly to say that our government is providing free aircon to poor people.

Technically, they do. But it's such a niche case. Just like people don't typically go and fill up jugs at the public water fountains to flush their toilets at home with.

So you are technically correct, but it doesn't matter.