THe DWP cannot just make a new Decision on your claim, so I suspect that a Recondiseration has taken place.
On this basis, and on the assumption the the original Fit for Work Decision was made as part of your transfer from IB, then I would expect their to be back payment from the closure of your IB claim to the date of the new letter.
Unfortunately, if you were talking to someone in the DWP call center, then what they say cannot be relied upon to be accurate or even applicable to your situation.
I would contact the DWP again to dind out what is going on.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems