There is no governing body that says what is correct or incorrect. I find the sentence to be unacceptable and arguably ungrammatical. If you change "said" to "said it", "spoke" or "talked", then it's okay. If you make that change, it is probably an epistemic use of "must", but maybe there is some far-fetched context in which it is deontic.

I can't make "said like" fly. There should be object, so "He said" is mostly ungrammatical, although there are some elliptical constructions like "You say...", and some idioms like "I'll say!" (but not *"They'll say!"). Other verbs like "speak, talk" don't strongly require an object, so "talk/speak like that" is okay. Similarly, *"If I gave like that" is bad, and so is *I gave" (with provisions for elliptical constructions like "I already gave").

I completely agree with what panini wrote above.

In Spanish, it's odd to say "I know" ((yo) se) without an object, so in response to something you might say "yeah, I know", as (yo) lo se (lit. "I know it"). In Engilsh, "say" requires some object: "say it", "say something", etc. Other verbs like "talk" and "speak" do not require an object. Just lexical variation.

I am not aware of any dialectal variation for this, but it's possible that in some dialects "say" may be intransitive (it sounds sharply ungrammatical to my ears), or perhaps examples you've seen are from non-native speakers. Or very specific contexts like panini mentioned.