No, that's not true at all. Police and prosecutors can't (legally) break the law to make a case.
If a citizen breaks the law catching another citizen breaking the law there will probably be charges for both parties.
Erica from the dentist's office didn't "blow the case" by texting the thief.
Finally - and this is the most important bit that everyone seems to be missing - Erica didn't commit a HIPAA violation. She used his phone number on file to text him, something my dentist's office does to me as well. She didn't share any personal information with a third party.
This is a gentle reminder that reading something in a meme does not make it factually true.
The person you're replying to isn't correct. Police and prosecutors can't break the law to make a case. If you exceed the speed limit while trailing a killer, they don't get to go free.