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In the artillery rules it says you have to draw line of site from the gun and from the crewman firing it.

If a mek gun is behind an aegis the crew is too short to see over it.

So in this case the gun cannot fire. (I think)

So, how can you legally place the crew so it can fire? I assume you are not allowed to put a gretchen crewman on top of the gun to get a better vantage point.

Am I right with how this works?

I believe you are right about not being able to shoot.

If you only have 1 gun you could put it at the end of the aegis with a guy sticking his head out to see.
You could also put 1 grot from each gun on the other side of the aegis to see, but obviously you then lose the cover save on those models.
Other than these I think you just have to find other cover for them.

Another thing you could do is what my brother does (with permission from the opponent). He has some grots modeled standing on boxes so they can see over, but they aren't allowed to move with their boxes and obviously it lets enemies see them too. If you just play casual games with the same group of friends over and over it may be worth asking if they mind you doing something like that.

Or lol...you have 1 or 2 poor saps standing on the other side of the aegis as spotters, as long as they are within 2 " of the gun it can shoot.

Can a crewman move a couple inches and then shoot the gun? (since its heavy)

I did mention putting some guys in front of the cover.
Not sure about moving and shooting as I don't have a rulebook on me, but I would think it would be able to fire but only snap shots as it moved and is heavy.

There was a really long thread on this, if you'd like to read up on it.