Think of it another way:

The CIA and NSA will do their things collecting foreign intelligence on largely non-US persons. They store that information in a database somewhere with a big old "foreign" sticker.

The FBI will do their things collecting domestic intelligence on largely US-persons, storing their information in a database with a "domestic" sticker.

Intelligence agencies will share information between each other at times when their jurisdictions cross and for certain interesting mission sets, but it needs to be a deliberate and measured act. The FBI shouldn't be able to just sift through the "foreign" database without any supervision for things that look interesting to them - they need to be granted access to a certain tailored box within the "foreign" database with extraneous information (to them) redacted or removed.

Additionally, there's a whole 'other can of worms on how much information they were able to access. It's one thing to catch an American committing tax fraud from their emails between a foreign bank lets say. What if an FBI agent knows their (ex) spouse has some overseas dealings and they want to snoop or find some dirt? They can't legally use their organic tools to find this information on someone they are connected to without probable cause, but who's to say their "foreign" database accesses account for the US person who isn't the focus of surveillance? They aren't looking for "Spouse, bank fraud," which would probably raise suspicion with supervisors, but rather "foreign banker, any conversations with spouse@hotmail.com," which the other 3 letter agencies probably don't care about.

Our issue here is that the FBI is using information that they shouldn't have access to. You can argue legitimacy one way or another, but the way these agencies are funded and authorized to operate necessitates this separation. The FBI may have had a valid case for querying and using this information, but only under through the proper channels, which it seems were not used.

Yes, that sounds right, except that I think it really is relevant that one party was a U.S. citizen.

There are strict laws against the U.S. government surveilling U.S. citizens without a warrant. By using FISA information gathered through warrantless foreign surveillance, the FBI appeared to be taking a backdoor around those laws.