...but the rotating beacon isn't used ONLY in IFR operations, is it? I swear I've seen ours on in VFR conditions...
You're right. Rotating beacon on during the day is not a regulatory indication of IFR. I remember a quiz somewhere along the way where the question was , "What doe a rotating beacon mean during the day." The correct answer was "a controller forgot to turn it off."
==============================
AIM 2-1-8(d) In Class B, Class C, Class D and Class E surface areas, operation of the airport beacon during the hours of daylight often indicates that the ground visibility is less than 3 miles and/or the ceiling is less than 1,000 feet. ATC clearance in accordance with 14 CFR Part 91 is required for landing, takeoff and flight in the traffic pattern. Pilots should not rely solely on the operation of the airport beacon to indicate if weather conditions are IFR or VFR. At some locations with operating control towers, ATC personnel turn the beacon on or off when controls are in the tower. At many airports the airport beacon is turned on by a photoelectric cell or time clocks and ATC personnel cannot control them. There is no regulatory requirement for daylight operation and it is the pilot's responsibility to comply with proper preflight planning as required by 14 CFR Section 91.103.
==============================
My answer to the OP instructor's question, which dealt with class D airspace, would be to listen to the ATIS or AWOS or, if it had neither (doubtful) to ask for the reported ceiling. If they reported a ceiling less than 1000', the airport was IFR.
If that wasn't the answer, I'd ask what the trick was.