This seems false in physics. Prestige of your institution matters. Prestige of the journal matters, too. Arxiv is fine, Physical Reviews is better, PRL is better yet. Nature/Science is so high, if you publish something that is not perceived as top-quality, you may get resented by others for status jumping. And there are plenty of journals which only get to publish second- and third-rate results.

Of course, the usual countersignaling caveat applies: once you have enough status, posting on Arxiv is enough, you will get read. Not submitting to journals can be seen as a sign of status, though I don't think the field is there (yet).