Moderator: United Airlines
Join Date: Jun 2007
Location: SFO
Programs: UA Plat 1.995MM, Hyatt Discoverist, Marriott Plat/LT Gold, Hilton Silver, IHG Plat
Posts: 66,836
The in flight request for medical help and the paramedics on arrivial were for two purposes
1) to make sure you did not have 1st or 2nd degree burn -- sounds like you did not - good;
2) CYA (of course) once you start asking for names and stating you are going to report this, it of course signal alarms of possible legal action. At that point it is their responsibility to protect themselves and UA by having adequate medical documentation of the extent of injuries. Just as your also desired.
Sorry you were injured, it should not happen but in human interactions things happen. I think it was poor form not to provide a first name and apology immediately but the more you press the more you began to look like a problem case. But even then it appears they attended to your medical needs in a professional manner.
If you are still concern, seek your own medical checkup.
My guess is someone from UA corp will do a followup to check on your condition and likely offer some goodwill compensation.