Actualy it is not that hard to understand, when they encounter Braxon at the end of the episode he mentions that he "did not experiance that timeline", however, there still was a Braxton on Earth at that time.
Later in Relativity they mention merging, or something like that, the three Braxtons. So here is what I figure happend, the Braxton from the resoted Sol timeline retrived the Braxton from the destoryed Sol timeline. As a result he now would have all the memories of having spent 30 years in the 20th century. There by making the statment in Realativity true.