Hi Vincent,
Sadly Greater Anglia are making things up.
The 60+ Oyster Card is an off-peak zones 1-6 travelcard with a few TfL related extensions. As a zonal and season ticket, the train DOES NOT need to stop where you change from one ticket to another. Please quote condition 14.3 of the National Rail Conditions of Travel to them.
If they’ve said this using public social media then please reply with the link and I’ll put them right publicly.