Yes SOU has the railway and the motorway, but that also means it's quicker to get to other airports too. Even so, I bet that the majority of outbound SOU pax originate either in Southampton or to the west and Southwest of the city. In other words people that are further away from LHR and LGW both of which offer a range of destinations, costs and frequencies that neither SOU nor BOH can ever dream to match.
So any story that has Flybe operating from BOH has merit, it offers Flybe more flexibility and a catchment similar to SOU, but with less risk from competition. Even so, the story is also likely to be the stick that is used by Flybe to negotiate better charges from SOU.
I live 30 mins northeast of SOU and, depending on the time of day, 30 mins southwest of LHR. All things being equal I would never go to LHR as an alternative to SOU - its not just the time to get to the airport, its the comparative hassle when you get there - always need to allow an extra hour at LHR regardless of terminal.
However I, and the population centres around where I live, am at least 60 mins from BOH and quite often more - for me LHR and even LGW are more attractive. There's a reason that BOH has never managed to compete with SOU and that's because it is too far from large population centres.