The two situations should not conflict. For 8889 reports contributions as well as withdrawals. Part 1 of form 8889 reports contributions, and whether or not they are deductible. Part 2 reports withdrawals, and whether or not they were for qualified medical expenses. Then the penalty for excess contribution is 6% of the amount of excess contribution, or 6% of the remaining balance, whichever is less, is calculated on form 5329.
There should be no issue with using form 8889 for someone who is not eligible, that's one of the purposes of the form. You will need to talk to the support people for whatever software you are using.
