I have the same problem, starting one Christmas Day when I took my watch off to put it on its charger when going to bed. It happened again the next day while sitting at a football (soccer) match, and I contacted Apple Support, who were very helpful and put a monitoring app on my watch - it had happened again without any obvious cause before they took that step. Of course it did not happen again within 24 hours so they took the app off again. All was well for about three weeks, when the alarm went off again while I was sitting at a football match (there had been a winter break but I had been at one match in between the two occurrences. This time the support guy just started again, didn't seem to have looked properly at my notes, and told me that the two options were to switch off fall detection (not an option when the main purpose of my upgrading to Series 4 was for fall detection) or to take it in to an Applestore to check the hardware. In between the call and the Applestore visit, the alarm triggered but this time it was a genuine fall when I slipped on the ice while curling, so I know that it actually does work. By the way, that advisor told me that sharing the diagnostics with Apple would not help my case but simply provide Apple engineers with data which they could analyse along with lots of other data about fall detection.
The watch passed all the hardware tests and the advisor told me that she thought it was a software problem. All she could do was set it up as a new watch, which she felt would solve the problem. It didn't - the fall alarm went off again the following evening, once more while I was sitting at a football match. Maybe something to do with clapping? There is a delay between the cause of the alarm and the alarm going off so I don't know what I had been doing - too anxious to turn it off before it called 999.
The Applestore advisor did not offer to exchange the watch as she said that if it was a software problem it would happen again with a new watch. My wife has a Series 4 and sits beside me at the football, and she has never had the fall alarm go off.
The original advisor sent me an email telling me I could reply to it if the problem recurred but when I replied after the last incident, no reply has come back after two days.