Be very very careful if considering investigatory/disciplinary action, get advice from ACAS and even legal advice, especially if considering dismissal, to make sure that you do everything properly.
I think the individual circumstances could make a big difference. For example, I know on my phone that, when a message comes through it is visible on the front screen without opening so could be read (at last the beginning of it) without anyone even touching the phone, say if it was left in plain sight on a desk.
What the message said could also make a difference as well, say if they saw that there was a message about a serious health worry like a cancer diagnosis where employees could have been worried, not just about jobs but about the employer personally or if something bad about the business (say something to do with potentially going under and job losses).
It doesn't make it right but there may be more to the circumstances that might not make it clearcut.