I ride multi-use trails a lot, and we all have to remember to share the trail. Yes, most of the pedestrians and many of the other cyclists are oblivious, but if you ride trails of that sort knowing that's what you're sharing the trail with, then you can be prepared to react when necessary. And, as Regina pointed out, you cannot realistically (or logically) use an MUT for fast training rides. Most trails do have a 15mph speed limit that should be respected.
The other thing that I learned a long time ago on trails of that sort: Do NOT run over anything that looks like a stick unless you are absolutely sure that it is a stick!