The existing timings for occupation of the Eastleigh - Fareham line are xx28-xx48 in both directions with the crossing move at Botley, so you could theoretically run an additional hourly service timed at xx58-xx18 without conflict. It’s just whether this would be better as an Eastleigh - Fareham shuttle or part of a longer service.Never a possibility IMHO. They never really explained how they’d magic away all the existing services…
The “Echo” probably should have written Southampton - Eastleigh and Southampton - Fareham separately. The way they’ve done it leads to assumptions about through services that just aren’t likely, once you consider both routes separately it becomes more realistic.
Then, the Botley line has already previously had a half hourly service in the peak flow directions. That’s not too revolutionary.