Well, if I ask this question without considering RLV,
Q: Can people read your private messages A: YES
You can use "Spy", an open collar app. This App enables consenting partners to spy on each other or in other words will allow full Owners to receive activity and chat reports on the collar wearer.
https://www.opencollar.at/spy.html
It also means a sub that you talk to might be relating the details of your discussion to his/her owner.
I hope this helps you.
Nin xx