For Vlad it seems to mean, if it's true for him then it must be true for everyone else.
Otherwise, God-dodging!
To be fair, I think it's a generally unclear phrase. My liking for marmite is obviously in a simplistic sense true for me. It is also though effectively true for everyone i.e. That I like marmite.
Rather it would seem to be about whether I think it is important for others to agree with me. And that's not really saying it's true for me as opposed to in any sense not being true for others. I suspect in most cases when people say it is true for them, they are also saying they think it is true for others. Else why believe it at all.
Vlad seems to be unclear about what he's is meaning but to be honest, I think that's true of a lot of the time it's used. I don't really see the value in it.