It's possibly because Wilts and Dorset (Salisbury Reds and More) is part of South Coast. There's more linkage and overlap between Swindon Bus and Salisbury Reds in areas like Marlborough etc (though it's less since a few tender losses). I don't think there's any connection between SBC and OBC/Thames Travel; think the closest they get is an hourly Wantage to Faringdon service.
It was my understanding at the time of the takeover (I was employed by the competition in a commercial role!) that Go South Coast (GSC) needed a substantial engineering facility which they couldn't have in Bournemouth, Poole, Southampton or Salisbury. Not just because of the lack of space, but also the supply of qualified engineering staff in an area where there are several train depots and hauliers offering much better terms and conditions. There are after all only so many people you can poach from the competition!
Swindon isn't considered to be too far from Salisbury and had the spare capacity to take on other jobs as the site (and it's facilities) was much larger than it needed to be for the operations running from there. Even after some people took voluntary redundancy post the takeover the site was able to take on a lot more work from other GSC depots.
Given the proximity of Oxford to Swindon it would be been more sensible for the operation to have fallen under them but GSC needed that engineering base.