I was advised by the insurance rep of the company's hangar Insurance to have my own liability insurance should an accident occur involving an engine I had released on condition.
No Hoper,
That raises some interesting issues if you were an employee of the organisation holding the Hangar Keepers policy. Depending on the insurance rep., if I was told that I would be looking into the matter very carefully -- and keeping my pen in my pocket until I was 110% certain of the conditions of any applicable policy. Having said that, insurance reps and some brokers are notoriously illinformed about the policies they are selling. For my sins, I spend too much time with lawyers, much of whose income is derived from aviation insurance disputes.
A possibly analogous situation is rental aircraft where, in the event of an accident, the policy holder (school?) gets paid out, then the pilot is sued by the insurance company for the payout, because the policy does not have a no recourse clause, but it is a bit hard to see how that can be applied to an employee. If your status was as a contractor, that is a different can of worms.
Tootle pip!!