I think the OP meant riding rides solo, as in without the rest of your party. However, I can tell you that my family typically rides Astro Orbiters in the morning and I find it hard to believe that the first thing people want to ride in the morning is CoP. So in this instance, yes, I have ridden it without ANYONE on the ride a handful of times, but not every time.
I may be wrong, but I took it to mean actually alone, as in no one else is on the attraction but you at all. There are alot of solo travelers at WDW every day, so riding without any other family present wouldn't be unusual at all. Riding an attraction totally alone, (with you the only one on the ride period) would be much more unusual.
I've actually done this twice on the same trip and both on fairly scary rides. I was at AK at rope drop one day, actually planning on rushing over to EE (like most of the crowd). For some reason, just as I came down that little slope from Discovery Island, I looked ahead and noticed everyone rushing either toward the Safari or EE and thought, what the heck, I'm not following that crowd. I decided on the spur of the moment to rush over to Dinosaur instead. No one was there but the CMs. As I walked through the queue, I asked the CM if I could skip the preshow. She laughed and said since I was the only one there sure, to just push the doors open and walk on down. As I was walking down the stairs, one of the CMs looked up, and said, 'Hey we have a customer'.

He then made a comment about how they never have anyone that early, as everyone always rushes to the Safari or EE first. He asked if I was sure I wanted to ride alone and then told me to pick any seat. I was the only guest in the entire attraction. Riding Dinosaur alone is a totally different experience than riding it with a vehicle full of other guests.
A couple of days later, I was over at Universal and instead of rushing to the Harry Potter ride over at IoA with the masses, instead I went first to the Studios and rode Mummy right at park opening. That early there was only a few people on it and as I was getting off, I asked the CM how to get back on it the quickest way. He told me to just cut through the baby swap area and I could get right back on in the area where express pass guests did. A couple of teenage girls heard him and decided to join me. When we got back there, there was no express guests waiting so we were the only three on the ride and got to choose our seats. As we got off, I decided to ride it a third time, but the two teenage girls had had enough, so I went back there by myself. Again no express pass guests were back there, so after waiting a few minutes the CM asked me if I was willing to ride it by myself and told me just pick any seat. I had the whole car to myself. Again it's a totally different experience when there are no other riders there with you.