The first statement is true. You can mine on all the chains you like. With 10 TB you can mine with full 10 TB on 2 forking chains.
You risk nothing of your mining capacity if the network forks.
This can only be solved with POW or similar concepts, as you literally work for every nonce you send every round.
To give you an excample, let's say Burst forks to abc and xyz. They are both equality accepted and people are working to improve their favourite chain.
As a miner, you want to earn as much as possible. Because of that, you choose to mine on both chains. You lose nothing, but just doubled your efficient capacity.