That's only true if they were ideal devices, but they are not.
I have not tried it myself, but from what I read if you leave two batteries connected in parallel for a while they will have less charge than if you had left them not connected to each other.
Batteries also don't discharge at identical rates, so each time you use them you will end up cross charging them, which wastes energy.
You are partially right but seem to lack some actual understanding of the underlying reasons why this is the case.
These are both new batteries that have been installed at the same time (without an O2 vent by the way, that is a serious mistake imo) and for all intents and purposes will simply function as a larger battery.
Even if they were not identical and not the same age they would still not do anything cyclical, but would function as a larger battery with the charge/discharge characteristic much like that of the older/weaker battery.
This is why it is not recommended to add a new battery to an existing pack, it will age very rapidly.
You do need a diode separator if you intend to charge your RV batteries from the regular alternator as well so that you don't end up trying to run your starter motor off the (usually) gell household batteries (they can't provide that kind of current), and so that you won't run your fridge/monitor/whatever off the starter battery which you will need badly to turn the engine over once you decide to move.
I have not tried it myself, but from what I read if you leave two batteries connected in parallel for a while they will have less charge than if you had left them not connected to each other.
Batteries also don't discharge at identical rates, so each time you use them you will end up cross charging them, which wastes energy.