No.
Simple answer: No. Possible answer: if the person doing your simulator flight happens to be an FAA instructor, the simulator is certified for landings, and it's part of a Part 142-approved program...
"I asked the FSDO" is not an authoritative source. FAA Inspectors are not always right.
61.56 requires an "authorized instructor." The FAA has defined what an "authorized instructor" is. Only FAA-authorized instructors may sign off on a Flight Review to maintain the currency of an FAA-issued certificate. There are some other options besides the straight "hour ground hour flying" flight review, but they also require FAA-certificated examiners, check pilots, instructors, or US military instructors, etc.
Is there anyone you fly with who is also an FAA CFI typed in something you fly? That person can give you a flight review. The airplane does not have to be N-registered, but the instructor does.