I guess that was the good side of the early technology. The 55 byte
peer to peer message was not saved on the server, there was no
forwarding capability and even with the type of message that went
through the dispatch system and was logged, disk space was so
expensive that they still got purged eventually.
These days nothing ever really goes away and virtually anyone with a
little tech savvy can see it. The other difference is these days there
are search engines powerful enough to find it in the clutter.
I don't know if text messages are saved by anyone other than users.
Can't imagine the phone companies want to be responsible for storing
the millions of messages per second going between teens.