Someone asked me this question recently.
Apart from the old phrase that “ATC are not police”, I have no idea what the formal answer is. At the ultimate level it must be Yes because if ATC are not happy with you they can instruct you to land (divert). It is not necessary to be intercepted by an aircraft for this; airborne interception is for use where you are not in radio contact, etc.
Over the years I have been asked whether I have oxygen (France), can a TB20 really fly UK to Granada (Spain), whether I have an IR (France), am I flying IFR or VFR (while sitting in CAS at say FL150, France, Italy, etc). But these were simple questions. I’ve never been asked if I am RNAV1, etc.
My weirdest ATC conversation was in 2003 where they asked for the pilot’s name and other stuff but without saying why. I gave them the answer but didn’t find out why until 5 months later 
Not a single “odd ATC conversation” was in the UK.
I have on one or two occasions heard ATC ask if an airplane was IFR equipped and if the pilot could accept vectors into IMC. This was in the US, but there was no negativity implied, the controller just wanted to know what he could do with the flight.
Same, I’ve had “can you accept vectors” a couple of times when crossing CAS VFR in the UK
Flying VFR Iwas sometimes asked whether I was IFR (France, Spain, Italy, Croatia) and whether I have oxygen (Spain, France, Austria). Quite regularly I had to acknowledge that I am VMC or that I have to stay so.
Never did I find that bad. It is more of a sign that they are thinking ahead for me.
I have no formal answer, but as far as “questions from ATC go”, I do get asked, for example, if I can fly DCT to a GPS waypoint. Despite filing the info in the flight plan (/G and a PBN spec in RMK). I didn’t ever think it was ATC questioning my capability, but that it was easier for them to ask and give me a shortcut than looking up the info in the FPL, or that they simply don’t see that information.
Same with “are you IFR or VFR” despite filing Z and picking up IFR 5m away from departure airfield, according to FPL. I just assume it is easier for them to ask/confirm, than look things up but still possibly have doubts, because the preceding controller didn’t update something, or has no way to pass that info. Never has it occurred to me they could be questioning anything.
ATC (to be fair, TWR, not en-route, so performance is not important) also sometimes think that the M20T ICAO identifier is a Polish version of the PA34 – the PZL M20 Mewa – I heard that as we did a low pass and the traffic waiting to line up asked about the plane.
tmo wrote:
ATC (to be fair, TWR, not en-route, so performance is not important) also sometimes think that the M20T ICAO identifier is a Polish version of the PA34 – the PZL M20 Mewa – I heard that as we did a low pass and the traffic waiting to line up asked about the plane.
When I was on final, I heard TWR tell departing Air France traffic they would depart after my landing and telling them “I don’t know what kind of plane that is, code is C10T”. I had enough available mental bandwidth to chip in and explain.
denopa wrote:
Same, I’ve had “can you accept vectors” a couple of times when crossing CAS VFR in the UK
It’s actually a reasonable question. A VFR aircraft could potentially have a wet compass as the only navigation instrument and then it could be tricky following vectors.
Quote I didn’t ever think it was ATC questioning my capability, but that it was easier for them to ask and give me a shortcut than looking up the info in the FPL, or that they simply don’t see that information.
My experience with ATC (both U.K. & Europe) is that if they ‘ask’, it is to help themselves and me:
“Can you accept a direct to Bordeaux (280 miles)?” It ascertains that I am RNAV equipped and can comply – without having to do any homework themselves.
Once I was caught out by Lille as I asked for the RVP at Calais (which I regularly do for renewal):
“Have you filed IFR?” I usually file ‘Z’, but had failed to do so this time. They claimed they couldn’t do a ‘Pop Up’ – something which I readily accepted.
Once I heard Deauville asking a ‘G’ plane: “Are you IR qualified?”
I suspected that he was asking for a procedure, but hadn’t filed IFR; or possibly, they have had U.K. pilots in the past using a IR(R) as if it were an IR.
Peter wrote:
I have no idea what the formal answer is. At the ultimate level it must be Yes because if ATC are not happy with you they can instruct you to land (divert).
Peter, you’re once more stirring some pot of nauseous stuff 
As has been pointed in some of the posts above, ATC questions your capabilities to best fit your in their system, nothing else. As an example, a few years ago asking us “are you RVSM equipped?” was not infrequent on the line.
Now assuming for example that a pilot displays such poor performance that his qualifications, or equipment are in doubt… the relevant ATC unit will alert the relevant police aka CAA, who would then come out and enquire. AFAIK nothing new here, ref for instance to some airspace infringement thread… who’s pulling your license? ATC?
Not stirring the pot. Someone asked me and I thought the Q was reasonable. Just take it at face value; no hidden agenda
