If I delegate to you, but you have no choice in how you execute the delegated task, then I don't have to trust you.
Not exactly. If I delegate to you, and your actions have no effect whatsoever on the system, then I don't have trust in you.
I didn't frame my response systemically. I wrote if "I" then "I". Yes of course for a node in a Byzantine fault tolerant system, the node can't deviate from the objective verifiable truth that is Byzantine fault tolerant. Precisely. Then the system doesn't have to trust that delegate.
Even that is not entirely sufficient. The node has to also be fungible, replaceable, and not able to monopolize its function.
And that node must not be capable of influencing the verifiable truth by collusion or any other means.
Actually it is not correct to state "no effect whatsoever". Even miners in Satoshi's proof-of-work have an effect; it is just that the effect is objective verifiable truth and Byzantine fault tolerant (within the tradeoffs of Satoshi's design).