I think they are not being truthfull it doesn't say that in my book of a Peugeot Partner which is akin in design to a a citroen Berlingo but bigger.
First try the following according to my Peugeot Partner book (Partner is like a bigger Berlingo).
Programming remote after changing batteries.
Switch off ignition (obviously you have to put the key in first and turn it on).
Switch ignition on again
Switch off ignition again and remove the key this should reset key remote.
Now if this works go to that garage ask for a written quote and send it to Citroen ask for email save posting. I've never heard of a on board computer needing re-programming just because you changed remote batteries, its more the key so the on board computer recognizes its the same key. if above works contact Citroen and report what the garage told you but try get a written quote first for evidence.
Citroen home site contact
0844 4ss63 3500
Citroen help 08000 72 72 72
Bob U.K.
December 2012