I too carry my own insurance even though I am covered under my facility. The bottom line is that if my facility can (in any way) find me irresponsible in any of my actions (negligent) than I am still covered through my own insurance.
Also as a professional it really states you are taking yourself serious.
Absolutely!!! Someone who is injured ‘could’ always still try to come after you personally even if you are training them in a facility. As ‘they’ always say, “anyone can sue anyone” even if it doesn’t mean that they would necessarily win, you want to be protected from the expense of defending yourself. For the extra $100+ that it takes to get at least minimal insurance for yourself – it is worth it.
I hope that this helps.