Criminal (or most civil) law protections are not relevant to FAA aeromedical, they are not conducting an "investigation". They are ADMINISTRATIVELY evaluating your ability to safely exercise the PRIVILEGE afforded by your ATP. Very few "rights" involved in that.
So there is utterly no proceedings or process which will "undo" their intent to evaluate your addiction/abuse status. You cannot get off on a technicality with aeromedical. With PBR you might possibly be able to do that on the enforcement side, but not medical.
One trigger for substance concerns with the FAA is an arrest and/or charges, no conviction required (they know that convictions are commonly dodged with legal technicalities or plea deals, which of course does nothing about any underlying addiction issues).
You need to understand that so you know where you stand.
That said, the real problem here is probably lack of BAC info (they don't have visibility on investigation details since there was no trial). If it was a 0.03 they would would probably just close the case. But they may suspect the actual number was much higher, and that you're withholding the info from them. In which case they'll assume the worst (ie severely impaired but not prosecuted for technical reasons), and throw the medical book at you. If you can get access to a BAC showing you well under DUI limits, that would likely make this go away.
The good news... if you can pass the HIMS stuff, they probably won't have grounds to deny a medical, without actual evidence of impairment.
Again, they are not interfering with your (non-existent) "right" to fly, they are evaluating your ability to safely exercise the privileges of your certificate.