Samsung technician is telling you what he has been trained to say (like a call center operator). It does not make any sense:
Think of the bigger battery as an extended battery and it will work as long as it fits in the battery compartment and the battery terminals are identical (if it is advertised for your model by a reputed seller, it should). This is not a unusual situation as after market battery manufacturers make a large capacity battery that serves for several device models as long as the battery dimensions and terminal connections are same.
It's no secret that accessories such as batteries, cables and other accessories are far more expensive from OEM compared to after market manufacturers (added revenue for them). Therefore standard refrain of buy OEM products only.
But, you would face a problem of correct battery reading in your status bar When you change your battery and replace with an extended battery, the ROM information pertaining to battery is not updated ( battery capacity is hard coded - for more details see Where are the battery capacity files located?).
So, your battery readings in status bar would be wrong. To overcome this problem, use 3C Toolbox and adjust the capacity of the battery manually in the app (from Battery Manager → Tap the 4 small square icon → Adjust Capacity or use Configuration Wizard) and create a shortcut on your home screen for the Battery Mgr widget and use that to measure (not the status bar battery status)