I've also had boats continue moving when in the driver seat and not touching the throttle. The only way to stop was to shut off the engine. Could be related? Something is definitely up with throttle controls for boats.

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This is currently the case with every boat in the game. It happens if you hold down the throttle and leave the drivers position, regardless of where you move. If you hold down the throttle while ejecting from the boat, it will continue forward on it's own.

I don't actually see this as a bug, just a bit lacking in polish. It's really quite convenient. For large boats with inboard motors, you'd expect the throttle to stay where you put it. It's not a car, it doesn't have a pedal that needs to be held down. Every boat engine has "cruise control". This is also the case with most small outboards and tiller controls.
All outboards and many inboard engine controls, will however have a dead man's switch, stopping the engine if the operator falls overboard or otherwise leaves the controls.

Personally, what I want is analog speed controls for vehicles, and I'll probably be making a feature request for that at some point. Though I'm waiting to see if the analog steering that was recently put in gets a follow-up.

I agree with Valcea, for the RHIBs with tiller outboard motors the current boat throttle system is good, but on things like the military Speedboat and other medium-size boats the throttle should stick.

This is a feature, pretty cool one too. Not a bug.