HSA Contribution Limit for Non-dependent child on family HDHP

Hello, I have received mixed information on this, including from my company's benefits administrators:

• I cannot be claimed as a dependent. I receive no financial support from anyone.
• I have been on my parents' family HDHP the entire year, and will be through December (am under 26)
• My parents have contributed to their own HSAs (though I believe this has no bearing on myself).
• I am now also covered by a self-only HDHP through work.

Based on this situation, I have told my employer I would like to contribute the family maximum of $8550 to my HSA. They have pushed back, asserting that not only can I not contribute the family limit, but since I am a dependent (their words), I can't contribute to an HSA at all.

I suspect the benefits administrators are confused. I don't believe simply being on my parents' HDHP, without any other financial support, would change my non-dependent status. Second, my understanding is that being on a family-type plan makes me eligible for the higher contribution limit.

Can anyone check whether this is correct? And also whether being on a self-only plan, in addition to the family plan, drops my limit down to the lower individual limit?

I found this blog describing the situation: https://www.kitces.com/blog/health-savings-accounts-hsa-dependents-children-age-26-hdhp-taxes-contribution-limits/