Picard stated in Generations that it could not be removed. Geordie states in Insurrection that it had been. I chalk this up to progress... Advances in capability eventually allowing Data to first turn it off at will (First Contact) and later remove it (Insurrection). There is no evidence to directly support this, but to your point his dialogue after Geordie reactivates him in INS leads me to believe Geordi reinserted the chip after bringing Data back online and removing the compromising memories.
I disagree with the assessment that Data's statement in Nemesis is a contradiction. It is very possible to have emotions and not understand them. I'd argue that this was the case for Data throughout Generations.