Our Fidelity accounts won't link to our credit union either (CU is Meriwest). Apparently the CU doesn't participate in some banking system that allows them to verify account ownership. I had a similar problem when trying to connect a Chase account to the same CU. When I called Chase they offered to set up a 3-way call with the CU to verify the info, but I didn't bother.
What I ended up doing instead was setting up the connections from the CU side. The CU made two tiny deposits into the other accounts and I verified those amounts and from then on I can move money both ways, I just have to initiate it from the CU website instead of the Fido or Chase sites.