Your musician friends are right - it is a bit off-tune. By design.

John Williams addressed this in an interview, and it was indeed done on purpose - to imitate the way the live music would sound in 1930s bar. See the bolded text especially:

JW: The cantina music is an anomaly, it sticks out entirely as an unrelated rib to the score. There's a nice little story if you haven't heard this, I'll tell you briefly: When I looked at that scene there wasn't any music in it and these little creatures were jumping up and down playing instruments and I didn't have any idea what the sound should be. It could have been anything: electronic music, futuristic music, tribal music, whatever you like.

And I said to George, "What do you think we should do?" And George said, "I don't know" and sort of scratched his head. He said, "Well I have an idea. What if these little creatures on this planet way out someplace, came upon a rock and they lifted up the rock and underneath was sheet music from Benny Goodman's great swing band of the 1930s on planet Earth? And they looked at this music and they kind of deciphered it, but they didn't know quite how it should go, but they tried. And, uh, why don't you try doing that? What would these space creatures, what would their imitation of Benny Goodman sound like?"

So, I kind of giggled and I went to the piano and began writing the silliest little series of old-time swing band licks, kind of a little off and a little wrong and not quite matching. We recorded that and everyone seemed to love it. We didn't have electronic instruments exactly in that period very much. They're all little Trinidad steel drums and out-of-tuned kazoos and little reed instruments, you know. It was all done acoustically - it wasn't an electronic preparation as it probably would have been done today.

I think that may be also part of its success, because being acoustic it meant people had to blow the notes and make all the sounds, a little out of tune and a little behind there, a little ahead there: it had all the foibles of a not-very-good human performance.