Where I live a contract may take out a permit for a homeowner, but it is ultimately the homeowners responsibility to have the permit. Before the town will sign off they will inspect the work, and by law you are not allowed to pay a contractor the final payment until you have an approved inspection.
I agree. I ended up getting both the construction and electrical permits for my pool.

My experience is that if contractors are unwilling to "pull" permits, it's usually because they have difficulty with meeting some part of the code requirements - although they might also be trying to avoid the permit fee (I can't remember what the fees were, so I'm not sure how valid this is). If you haven't, you might investigate further what the particular issues the contractors have.