Incorrect.

In 1991 the League Banned the use and possesion of Steriods. The players union didn't want the league to actually test any of the players, and the Commisioner gave into those demands.

Even if that wasn't the case- it doesn't matter if it was specficially stated that it was illegal because of the Best Interests of Baseball clause. And to top ot off, the Commisioner doesn't need to have an admission or a conviction in a court to be able to act.

Because you bring up Pete Rose, and mention that gambling (on baseball) was banned long before he did it

At the start and end of the 1919 season, there was no rule specifically making it illegal for players to bet on baseball. During 1920, the eight Chicago White Sox Players, Shoeless Joe Jackson, Chick Gandil, Swede Risberg, Buck Weaver, Happy Felsch, Eddie Cicotte, Lefty Williams, and Fred McMullin were cleared of any charges by a grand jury at the end of 1920, yet Kenesaw Mountain Landis banned all eight of them for life from baseball in 1921. None of the players addmitted at the time that they were involved in the fix - although Buck Weaver admitted knowing of the fix, but denied any direct involvement (being paid or trying to throw the games) in it. Fred McMullin got banned for pretty much the same since his playing time in the Series was limited to 2 pinch hit at bats and no playing time in the field. A few players admitted having a direct involvement in tossing the games - but that was years after already having been banned for life from baseball.

Those players were banned, and Landis made it illegal from that point on for any player to bet on baseball games, conspire to fix the outcome of any baseball games, or to fail to inform the manager or owner of the team if they knew of any players betting on or conspiring to fix baseball games.

As for any records -
A couple of thos players still hold (either by themselves or jointly) records in baseball. Being banned from the game didn't remove what they did on the filed prior to it. But those records are obscure and have no signifigant meaning either.
The single season Home Run record has always been overrated in my opinion - no one talked about it during the '80s.