When you consolidate all of your student loans doesn't that mean you are paying interest for one?

After college I consolidated and deferred my loans. I was under the impression that when you consolidate all of the student loans it becomes one loan and therefor you are paying interest for just that one.

I get a statement in the mail since it's almost time to pay it tells me that all of my loans have been accruing interest. I call up Salie Mae and the tell me loan consolidation is when combine and have one payment but all the loans accrue separately. Is this correct? If not who do I contact about this?

TL;DR Salie Mae told me loan consolidation means you have one payment but each loan is still accruing interest separately. Is this correct if not who do I contact?