I started BuzzerBeater during the 12>13 offseason, so I might be biased based on the fact that I didn't take over the team mid-season, with a record already in place and all.
But, from my understanding, even if you register in the middle of the season, your roster is composed of new players, not the ones from the previous owner.
So my suggestion is that when you go to a team's stats page, and you scroll down to "Best Performances", those should only be based on the players that were on your team when you were manager, not players from previous owners.
I understand that for technical purposes, your team id is recycled from a bot team, but in my opinion, my team, or any team for that matter, is not the continuation of the team previously linked to the same team id. You don't take on the players, neither do you take on the budget of the old team. It bothers me that when I go to my team's stat page, I don't see the best performances of the players that actually played for me.
On the league's page, however, I totally understand why some retired players are holding some of the best performances, even if their manager is not playing the game anymore, because I believe there is some kind of league-wide continuity involved there.
I just want to say I love the game, and I'm not dissing by any mean, so if I missed a point, please discuss.
"Air is beautiful, yet you cannot see it. It's soft, yet you cannot touch it. Air is a little like my brain." - Jean-Claude Van Damme