Just to add - "backing" a policy or idea does not mean
pretending it came from you. In fact there are situations
when acting as though the idea came from you would definitely
be viewed by the board as a bad thing - taking credit for
something you didn't do yourself. Remember that even if you
don't agree with some of the policies, the board itself most
likely feels that all of its ideas are good ones, and they'd
probably like the credit for those ideas to go to themselves,
not to you.
On the other hand you should not say "this was their idea,
and I think it's terrible." But in the scenario you gave
that's not what was stated. There's nothing wrong with saying
that something came from the board, or that it cannot be
changed. And there are also definitely times when you would
want to say to someone who was complaining about a board
policy, "I totally understand where you're coming from, but
we have to follow the policy." This is being supportive of
the teacher while also backing the board at the same time.
Nothing wrong with that.
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