Do I have to say I have a HDHP since my short term disability company paid into an HSA, even though I don’t have an HDHP and I also don”t have an HSA?

No, you should not say you have a High Deductible Health Plan if you do not.

Your short term disability and a HSA are not a replacement for a HDHP.

Please contact us again with any questions, and provide some additional details.

It can't both be true that your disability company "paid into an HSA" and that you "don't have an HSA."  Do you mean some other kind of health care account, like an FSA or an HRA (health reimbursement arrangement)?

If anyone made contributions in your name into a true HSA (health savings account) but you were not enrolled in a qualifying HDHP, you will owe a penalty on those disallowed contributions, unless you remove them before the deadline.