Story mentions the Stones were recording two blocks away (in London). I checked the Zentgraf website but there is no mention of them recording in London around in the summer of 1979.
According to [timeisonourside.com] the Stones weren't together in early June. Not every waking moment was chronicled yet there's the time Charlie fell asleep in a restaurant, Keith reports to his probation officer and Mick is in court - quite a bit of nothing to do with music things and, obviously, the Stones not being together.
Not impossible at all, especially if it wasn't even the full band and they were using the Mobile. They were very much around London during the period. Mick's divorce proceedings, Charlie playing at Glyn Johns' wedding reception, Mick playing at Eric Clapton's wedding reception, Keith was at Redlands, Keith played at a wedding reception all in the timeframe of what might be called Summer. It was likely a chance to playback tapes from Compass Point or maybe after the Pathe-Marconi sessions.