Shallow dismissal. Singapore discriminates against LGBTQ couples as a matter of policy. Just because it doesn't affect you doesn't mean it's an anecdote.
https://the-singapore-lgbt-encyclopaedia.wikia.org/wiki/Publ...
In any case, it doesn't change anything, if Singapore is oppressing LGBT people they will do so government owned housing or not.
It's an anecdote for your argument. If the argument was "did Singapore discriminate against people through housing" it wouldn't be. If the argument is "should we have public housing [here]" then it's an anecdote. You'd have to show that this would happen in the place in question. If you want to make a general statement, you'd have to make that clear and make the case that in such countries landlords wouldn't discriminate against you for being LGBT (which they absolutely do).
Your definition of ‘anecdote’ seems way off to me. We’re talking about an objectively verifiable data point. Just because it doesn’t fully confirm some argument that someone’s making doesn’t make it an anecdote. Check the dictionary definition.
The definition of 'anecdote' has nothing to do with arguments. 'Anecdote' isn't a back formation from 'anecdotal argument'.
There's also the Fair Housing Act exemptions, where small private landlords with fewer than about 4 units, or landlords that share buildings with their tenants, can ignore the discrimination limits imposed by the FHA.