you should've told your friend the right answer. it may not have been said plainly in the film (since as you mentioned, the tutorial sessions were cut out) but there is a quiet moment between Dr Cornelius and Caspian that alluded to the old stories that molded Caspian to the man he eventually becomes:

Prince Caspian: Why did you never tell me about my father?

Doctor Cornelius: My mother was a black dwarf from the Northern Mountains. I've risked my life all these years so that one day, you might be a better king than those before you.

Prince Caspian: Then I have failed you.

Doctor Cornelius: Everything I told you, everything I didnt, it was only because I believe in you. You have a chance to become the most noble contradiction in history - the Telmarine who saved Narnia.

that entire sequence actually makes little sense to anyone who hasnt read the book. but the convo is there and therefore you can tell your friend the backstory to Caspian the way it should've been told.

The nights with Cornelius in the tower were one of my biggest disappointments of the film. I REALLY wanted to see that, and it really left some depth out of the film.
Like you said, gP, without Caspian's longing for the old days, and his wish that he could live in Narnia before Telmar conquered it, he is merely another power-hungry Telmarine who will use the Narnians to get his throne back. Yes, he'll be thankful to the Narnians, and he'll make it so they don't have to hide anymore, but he will not restore Narnia.
I agree with JadistarkilleR that you should have told your friend the real reason. If people don't get the deeper meaning behind these things, they'll get turned off and won't go see VDT, and then VDT won't do good, and then SC will never be made. Plus, your friend will carry these deep themes with him all of his life, and he will benefit from the story more than the franchise can benefit from him going to see VDT.

I agree, the story should be told as accurately as possible.It is impossible to fit everything on the screen, but while reading the story it is a big part of the movie that should have been added. I know there is so much you can fit on screen, but some of the other scenes we could have done away with.

He should know the true meaning of the story, so he will learn to understand it.

I think the scene with Cornelous atop Aslan's How comes too late in the movie to have any significant effect. Had this been established earlier in the movie (as it is in the book), the scene with Caspian at the Dancing Lawn would have been far more powerful.

Just another unavoidable side-effect of adapting an extremely uncinematic book.

I understand your point gP, but don't forget that there was an earlier scene where Caspian's lessons with Cornelius are alluded to:

Miraz: And what does Caspian know of this horn?

Dr. C: Your Majesty forbad me to tell the old tales.

Miraz: So I did

Guards come in to take Dr. C to prison, thus implying that he had taught Caspian the old stories.

Dr. C: I will say this; if Caspian does know of the deep magic, your Majesty has good reason to be nervous.

and what about:

Nikabrik: How do you know so much about us?

Caspian: Stories!

Trufflehunter: Wait a minute. Your father told you stories, about old Narnia?

Caspian: No, my Tutor.

(Forgive me if my quotes aren't word perfect. I did them from memory.)

These may be too quick for our liking, but the indication is there.
Plus, you could always pop in the video game if you really felt the need to explain thoroughly.

Exactly. True... there should have been more background story to explain it more to those who haven't read the Chronicles. But the movie does include scenes where it is fairly, even if not completely, evident that Caspian has been raised to think and feel this way by his professor. Which would also say that maybe the reason he's so different from all of the other Telmarines is simply because he knows a lot more than they do. After all, in the movie, Lord Sopespian to name one, didn't even know who the Kings and Queens were, which says something about what we're to believe they were taught about history and who the Narnians really were.
Although, if the filmmakers had just stuck to the story in that respect, it would make explaining so much easier.

I think he's not like the other Telmarines because of the influence Dr. Cornileus had on him by telling him the Narnia stories.

The movie made it hard for people who haven't read the book to figure out why caspian was nice.

I think GP that you should have told your friend the real story so that he would know where the movie was coming from. If he doesn't know anything about where the movie came from than he will not be a good judge about where it went. I say this because all the people before me on this thread are picking up where in the movie it does mention that Caspian had a deep knowledge about the old stories and clearly wanted them to return. They picked up on them because they had an understanding of where it came from. If your friend knew where the movie came from he might start to pick up on those things as well.

They actually filmed a scene with Cornelius talking to Caspian at night. It was cut from the theatrical film but it's an unlockable feature in the videogame. You can probably find it on youtube. Agreeing with the others though who've said it doesn't make much sense if you haven't read the book. The hints at his background in the film were very subtle. What I really wanted to see was the scene in the garden with Miraz. I do feel that for someone who has read the book Caspian's backstory was there just enough. Can't say the same for someone unfamiliar with the book.