I've had this conversation with several captains and they have all told me the same thing; they never want to leave anyone behind, but it's all about communication. If the people who are going to be late are not in communication with the ship, then the captain has no alternative but to leave them.
The number one reason anyone is left behind is NOT because they were on an independent excursion. It's because they either did not make sure their watch was set to ship time and check it regularly, or they were in a bar, got a little drunk, and forgot what time it was or what time the ship left.
This is why I always highly suggest people take the daily newsletter with them when going into port. It has the local port authority contact information on it and should something happen, you're able to get in touch with the ship.
Any reputable independent company is well aware of this and will be able to get in touch with the ship, but it's always advisable to take a cell phone just in case. You could just be walking down the street, trip, break an ankle, and have to go to the hospital - this would cause you to be late and it had nothing to do with an excursion. As long as you take the normal precautions, you'll be fine. We've done independent excursions all over the world, including China, and have never had any problems.
So don't let people scare you into thinking that taking shore excursions through the cruise line is the only safe way to go - it's just not true and there is absolutely no proof to the matter and no statistics to back up the claims. Besides, there are been many reports where thieves have specifically targeted cruise line excursions because they know all about them; when, where, how many, and who.
Of course, the cruise lines encourage this fear because it's better for them. They make alot of money on excursions. As an example, we wanted to book the motorcycle tour around Aruba. Cruise line wanted $355 per couple; the local Harley dealer only charged $155 per couple. There were 6 couples on the tour; 4 of us booked with the dealer and two couples booked through the cruise line. We were all on the same tour together! Guess who had more fun; those who paid $155 or those who paid $355? We booked the helicopter/dog sled tour in Juneau; paid $125 less per person than the cruise line charged! I could give you hundreds of examples, but you get the point.