There's an interesting reference in The Parish Councils (Model Code of Conduct) Order 2001. Prejudicial interests paragraph 9 includes the following:-
(2) A member may regard himself as not having a prejudicial interest in a matter if that matter relates to—
(a)another relevant authority of which he is a member;
It's not specific to the situation you've outlined, but if I were you, I'd ask the District Council's Monitoring Officer for an opinion on this.
You mentioned that they refuse to comment, so I presume they also refuse to vote. There are several references in guidance (but not legislation) to the concept of abstention being a last resort, to be used sparingly and the need to express an opinion, however challenging that may be.
Hope this helps.