Friendship doesn't have to be a one-for-one equal transaction. Part of what made this episode better than I expected was that Mariner had reasons to be supersuspicious that were not related to "I'm openly/secretly jealous of Boimler." The fact that a shapeshifter literally ate a close friend of hers by posing as a too-good-to-be-true partner in her past and the PTSD from that event helps explain why she would be so determined to prove it. Boimler doesn't have anything like that in his backstory (as far as we know), so he wouldn't be suspicious or motivated like Mariner was. Plus, his personality is not the badass rogue, so even if he did become suspicious, he would have done things by the book: notify Lt. Shaxs and/or the Vancouver's security chief to investigate whether Barb was an intruder of some sort.
I would say Boimler has proven his friendship by not ratting out Mariner for her many, many breeches of Starfleet regs or general rudeness (bringing contraband on the ship, stabbing him in the leg, sneaking Starfleet farming equipment without express authorization, drinking margaritas and bloodwine on the job, failing to follow mission parameters and drop K'orin off directly at the embassy, her rocking the ship so hard, stealing senior officer replicator privileges despite her demotion, probably missing some) despite having been given a direct order to do so.
Doing something that goes against his nature and that could get him in trouble if it were discovered is friendsip, through and through.