At our shop as a matter of policy any extra batting or fabric is returned to the customer with the quilt. Many people use the excess fabric for binding, as you anticipated.
However, as others have said, it is often necessary to trim down the backing and batting provided in order to load it on to the machine properly - so the trimming you describe may be down to the original size of the fabric. That said, I would always recommend providing backing and batting that is a bit more than you think is needed in case the fabric needs straightening due to the grain being off (rather than providing exact size fabric/batting which could cause problems - the longarmer can take it off to achieve the right size but can't add more on!).
As a general rule with us the quilt is given to the customer as it came off the longarm - no "post-quilting" trimming is done. If a customer requested trimming we would assume (tho would ask!) that they meant for it to be trimmed so that it was 'binding-ready' rather than having to trim again.
And there is always the possibility of oversight - it happens to us all!