I have previously bought MedJet but have not used them.
I had a recent experience with Allianz and also spoke with them after my experience. I broke my wrist in Canada and needed surgery. Before speaking with Allianz, I decided I wanted to have surgery back home and told the doctor that. I obviously was not an "in-patient" category or life threatening.
I called Allianz and told them I wanted to go home for surgery. They were amazing how quickly things went into motion and within 48 hours, I was on a plane back home (over a holiday weekend) with a medical escort. I have only positive things to say about this.
I later called Allianz and was asking if MedJet was also necessary. I know they are probably biased but one can't travel with just MedJet alone for medical and my healthcare insurance home doesn't cover me outside of the US well. Allianz told me that they will do everything possible to get you home so you can have medical care back home, if that is possible. They indicated that most want to be cared for by their local doctors and it is many times cheaper for them to fly you home than put you up in a hospital over seas. Granted that example can't cover all examples and if you are severe enough and need medical care overseas - it makes sense to do that right away (heart, appendix, etc..). If it is a broken limb like I had, they are going to try to get you home for care. I appreciated that info.