Interesting. My Mustang started itself. Luckily it was on the street when doing brakes on the Mazda 3. It has a remote start that has an off switch. Good thing it was not in the garage at night!
I had this issue with the Escalade when we got it. It came with some weird brand (Titan...apparently only available in Alberta) brand remote starter and two remotes. Truck randomly started itself while in the driveway a couple times, once at like 2am and a neighbor noticed and came banging on our door...
Anyway, I investigated and learned that the remote start system had 'slots' for four remotes...Since we had two remotes programed, there were two 'empty slots' because of that the system was 'open' and susceptible to interference from other signals like garage door openers or whatever. So I programmed both remotes twice, filling all the 'slots', and never had anymore issues.
Eventually, the two remotes we had got pretty beat up and were failing, replacements were unobtanium, so I found a well-reviewed car electronics place and had them swap the old system out for a modern Compustar system.....Nicer remotes, better range and peace of mind. Money well spent at the end of the day.