she initially posed as a State Department officer, using an Official Cover (OC, referring to a cover which involves another US government agency and thus provides diplomatic immunity). Then in the early 1990s she reportedly adopted a Nonofficial Cover (NOC, aka “deep cover”, referring to a cover involving a non-government CIA front such as a fake business entity), posing as a member of an energy firm operating out of Belgium.
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Posing as either a State dept. official or working with some firm in another country automatically makes you a CIA operative in the eyes of any foreign intel service. I think really these NOC classifications server more to protect their idenity in this country rather than protect them from coming under suspicion of a foreign intel service since they know all the games the CIA plays.
Yes, I'd think the CIA assumes any US embassy personnel abroad are going to be operating under the scrutiny of other intelligence agencies (especially in somewhere like Brussels, where Brewster-Jennings was based). The main advantage of official cover abroad seems to be not any added secrecy, but the ability to hide behind the embassy's legal shields under official and unofficial international agreements (which is the same reason foreign intelligence agencies often operate out of embassies and UN missions here).
I think a more telling area for covert/not covert research would be to find out when she was issued a sticker to use the parking lot at langley.