First of all as
@phoenix pointed out above, even normal non diabetic stable levels of blood glucose cause a positive impact on HBa1c. Even if hypoglycaemic levels left no positive contribution to glycation of haemoglobin, that wouldn't be relevant. Clearly, normal target ranges (and presumably at least part of the sub target range) make a contribution to glycation and thus to HBa1c.
The further logic is, even if low blood glucose levels did not cause any accumulation of glycosylation of haemoglobin, low blood glucose levels would still affect (reduce) the aggregated HBa1c value.
So in that sense, it is *similar to* an average, in that a middling value of HBa1c could reflect a middling value of blood glucose over 90 days, or it could conceal a mix of too-high and too-low blood glucose over the 90 days. In that sense I don't think it's totally incorrect to call it an "average" in the non technical sense of the word. A better non technical word to use for HBa1c might be that it's an "aggregate". But it doesn't change the essential point that an on-target or normal HBa1c *may* indicate a mixture of above-target and below-target (hypoglycaemic) blood glucose periods.
Coming back to the original question, in my view HCPs are right to *investigate* low HBa1c but wrong to *assume* it implies hypos in every case. The first thing they should do is look at the meter averages and the meter SD (standard deviation). If the meter average matches the HBa1c and the SD is good, the patient should be congratulated, and studied as an example of success. If the SD is bad, then give the advice to relax the tightness of control. If the SD is good but the meter average does not match the HBa1c, that's an ambiguous case. If a CGM isn't available then the patient should be asked to test more frequently and at regular intervals through the day, to see if there are lows that aren't being recorded by the meter but which are being 'recorded' by the HBa1c.