No, it was definitely not true in the past and is not true now. First, technically there is no much difference between a given app self-hosted by you and hosted by a company charging you for that except that in theory they should worry about these things instead of you. In practice, your experience will vary - companies happen to be as vulnerable as you, and for various reasons their reaction time might be longer.

Second, bugs are found every day, and your best bet is to use automatic security updates provided by your distro. Yes, if you host anything, you need to be a bit of a security guy and a small amount of paranoia won't hurt. But to say you must not self-host for security reasons is a gross oversimplification.