It is entirely normal and standard procedure to deice the aircraft immediately before departure, i.e. with all passengers on board and doors closed. The purpose is two-fold: to remove ice and snow deposits, and to apply a protective fluid that will give protection against further precipitation before take off. It is a single step process at European airports.
It is an uncommon event to have to return to the ramp for further deicing. You have to be very unlucky - severe conditions combined perhaps with a runway closure for snow clearance. The risk is minimised by using deicing fluid with suitable holdover times and carrying out the operation with the minimum time interval before departure.
Deicing is not carried out on arrival. The only occasions when it may be carried out well in advance of the boarding process is following a night stop (or similar long period on the ground) when there is a need to remove accumulated deposits and there is no risk of further precipitation. Clearly this was not the case with your flight.
So the phrase "re deice" is nonsense, as I think you have detected. Quite likely deicing was a factor - delays due to deicing are not uncommon even at the better equipped airports (I have no recent experience of GVA) and there could have been complications like crew hours as already suggested. Maybe the passenger agent had failed to understand the exact situation, or just tried to simplify a more complex picture. But to come up with a phrase that was so easily challengable seems just plain dumb.