They don't care about the health insurance. They WILL care about you not having done a TM30 when you go to file your first 90 day report (which is due 89 days from the date you stamped IN to thailand).
I'd say read this article I wrote on how to "self file" a TM30 on your own then when you go to do your first 90 day report file a TM30 first, (pay the 800baht fine) and then go file your 90 day report.
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