Hi!
My a1c is in the same area as yours (34 in Nov, 38 in Jan) and my nurse was telling me the same thing! I DO NOT have a lot of hypos, have good hypo awareness, but I also use a CGM to help me manage my levels better. My nurse didn't believe I could get my a1c this low without having constant hypos! She was only convinced when I brought a week worth of my graphs from a CGM showing no hypos at all.
A1c in the 5% area means you're in around 5-6 mmol/l most of the time and manage to keep spikes to a minimum (and/or bring them down fast) - and that's how it works for me.
So, you're not alone
Diabetes is a lot of work and it's different for everyone - for some it's harder to control, that's just how their bodies are. I think most medical professionals are just not used to see people being able to control their levels so well. But with more and more knowledge and places like this forum, I think recently people have been given more tools to actually be in charge.
I'm on basal-bolus with Levemir and Novorapid. I'd love to get a pump, but with a1c this low, I don't think I stand a chance. I'm no genius!
BTW, I don't listen to "most people" argument... my dietician says that 8 mmol/mol of fasting BG is "very good" for "most people". So if "most people" have levels this high, no wonder that their a1c is much higher.