When the gas-burner isn't running, if the house is super tight, and atmospheric drafted gas flue could be the lowest impedance path for the huge air volumes being drawn out of the house by the fireplace, as you suspect. Even if there is sufficient make-up air for the gas burner, there may not be sufficient make-up air for the fireplace. A temporary solution (and not a great one) would be to crack a window an inch or so on the first floor whenever you are using the fireplace.
Houses in MN tend to be tighter than the national average, and a big gas-burner can sometimes depressurize the basement sufficiently to pull air/smoke through any air leakage in the firebox of the fireplace, even if it's not actively backdrafting the fireplace flue, and even if there is a reasonable amount of makeup air via the whole house for the gas burner. The fireplace cleanout trap is the most likely air leak between the fireplace & boiler room, but there could also be cracks (large or small) in the masonry.
An open hearth fireplace (even one with glass doors) is a grossly inefficient thing, that sucks more cold air into the house than you would ever believe. The best you'll ever get out of them is 15% steady-state efficiency, most run less than 10% steady-state, and if you light fires then let them burn out it's usually energy-negative in locations at cold as MN.
The best solution (but not very cheap) would be to install an air-tight woodburning insert into the fireplace, one with a big viewing window door. Better still would be an insert that accommodates ducted combustion air kit. That isolates all air-currents between the wood burner and the gas burner, as well as from the conditioned space air. EPA rated woodburning fireplace inserts run north of 75% steady state efficiency (many north of 80%), produce far less smoke while delivering substantially more heat, and without creating drafts/backdrafts by pulling large volumes of air out of the house.