Well, there is a big image below, visually more impactive than the pasted paragraph, that goes "Messages from bigger services #do not# display their numbers". Yes, but neither do scammers.

You are trying to discriminate legitimate entities L from impersonators L̅ through properties P, and especially define ways to identify L̅. You state that P(L), but that says nothing of L̅. And in fact, it is P(L̅) also - logical exhaustion.

Logically the sentence works, because it implies "If messages display their numbers, they are not from bigger services". But in terms of effectiveness in communication, if put in the context of "how to recognize a scammer", the original may be misleading - because there (see the picture) you are focusing on the alphanumeric, not on the number, and the alphanumeric is not a criterion - the number is.

The intention was to state "do not trust numbers". But in that context it is important to stress "do not trust alphanumericals either".