'You would have to have some pretty weird stuff in an Access 2000 database that would prevent it working in 2003.'
So I take it that you can see from where you are sitting that there is none in the application in question?
No, of course not.
It is perfectly possible that the consultant is just trying to bamboozle the user with some techie words and there is no reason why the app would not convert.
But there are hundreds, if not thousands, of MS and 3rd party addins available and the use of any one of them in an Access app might inhibit conversion. So the consultant' comments could be valid. Unless you look at the app and/or try to convert it, you can't reach any conclusion.
And A2003 imposes more constraints on what is acceptable design in security terms so things which did work in earlier versions do not work any more.
I am thinking particularly of the use of several of the built-in functions in object properties (which appears to be a more widespread practice than I ever realised, as i don't do it at all!). These have now been re-classified as dangerous and cannot be used in object properties which means the app requires (usually small) changes to the design and code.
If I were the consultant and said the app will not convert simply and the user tried the app in A2003 and it ran perfectly, then I would not expect a profitable ongoing relatonship from then on would you.