Take this random and anonymous internet advice for what it is worth to you, but you are 100% correct. In fact, you could use your HSA and more (which would be tax deductible as a medical/health related expense) to cover all your bike related purchases so long as your physician writes you a letter/prescription yearly where it clearly states that in order for you to maintain your healthy current status you must exercise vigorously as done in cycling. He must also state that he recommends cycling specifically noting its cardiovascular, weight control/management/benefits, and muscular benefits. He must also clearly state that in order to do so, you must get appropriate accessories and equipment that includes/covers the activity safely and appropriately. By the way, this includes clothing, parts, tires and other wearable stuff, gym memberships and costs, etc. Racing? multiple wheelsets? Likely not.

Limits of this? Use your judgement and consider how you would defend it if audited.