Yes, I think your elderly ATCO was correct. I believe the limiting factor was the distance from the main radar heads. In later years the radar data from Ash and Ventnor was brought in by microwave link to some hefty dishes on that distinctive tower at West Drayton. Luckily, the technology improved by the time that the newer radars were introduced (PCD etc) so that landlines became an option. Without that breakthrough I guess that we'd still have JATCRUs at Sopley, Watton, Lindholme etc!!!
As a side issue, I suppose the fact that the ATCOs/ATCAs all lived in the greater-Heathrow area in those days helped make the decision. I mean, who in their right mind would move a new centre miles away and upset the staff ????