The only way to prove it to yourself is do it for yourself... I think that gos for psychic abilities aswell.
From my experience astral projection feels a lot different from lucid dreaming but thats just me. You have 360 vision in the astral and its very confusing i still haven't got the hang of it. Movement aswell is tough but i think thats because i haven't been able to get very far from my body and there is some interference going on.
I think the reason people are so afraid of AP is it opens up a hole different view on reality for them and they don't want to even go there or consider it... I even find people are scared of lucid dreaming and thats just a playground.
Another thing about AP is the intense vibrations you run into on the exit and that can be very intense and even scary, another reason people would stop as soon as they begin to project. Its a unreal feeling that you have to experience for yourself to believe. I can see why people who are afraid of that can of worms would feel better to write it off as lucid dreaming. I accept that its possible that its all in my head but i doubt it from everything i have read and felt. I will look to validate it for myself as i get more experiences but i'm going to need more practice thats for sure.
Here is a good link to start if you are serious about learning to project his book astral dynamics is great. The forums have some interesting discussion on the subject aswell. Astral Dynamics | Astral Projection, Energy Body, Healing, Kundalini, Auras, Self-Defense
I have wrote on this forum a bit about my experiences so far with AP and dreaming you can check it out here... i warn you the posts are long Astral Projection
I am definitely not "experienced" on the subject but i have had some interesting experiences and did a fair amount of reading now and i find it all very fascinating.
Peace and love