If I am not wrong, some of the BBL franchises are partly owned by Indians (but not by the IPL franchise owners). I agree that they don't have any involvement yet in BPL and PSL. But this can change. We have seen how fierce was the competition to get ownership to the two new franchises when the auction was announced. In the end Goenka and Citicorp won the bids, while Adani and Glazer failed in their attempt. Those who failed to win the franchises have two options - either they can invest in leagues outside India, or they can invest in state-level leagues such as the TNPL.
IPL owners do wanted to invest heavily in BBL but i guess CA didn't gave any permission, situation might change in near future if they head towards privatization. Atm BBL's teams are owned by CA and state bodies.
They also need to think about their own national players participation. Also the way IPL owners are investing everywhere i think some Indian players might start playing in other leagues too, may be not national contracted players but it's possible for un-capped talent.
But we all know that whenever India finds something very worthwhile, they want to make it private. They make everyone feel like that player or anything they are doing is premium stuff. So I don’t know if BCCI is preparing to allow Indian players to play in another league. But about ownership, I am quite confident that if the IPL owners are given permission they will also own teams from DBL. But so far, I don’t think that is going to happen.