It perhaps should be noted that if you look on
BaseballReference.com that Ty Cobb is still the career Batting Average leader. This is because Baseball Reference has different minimum standards than Major League Baseball, and Josh Gibson's 2,526 Played Appearances does not meet their 3,000 minimum PA threshold.
As for the argument that the Negro Leagues were not Major Leagues, you may wish to consult the collection of essays titled "
The Negro Leagues are Major Leagues" by Baseball Reference and SABR. It can be found online in its entirety here:
https://www.baseball-reference.com/articles/
The essays explain how there are 7 Negro Leagues that have been deemed on par with the white MLB and therefore stats are considered only from those 7 Leagues.
As the essays detail, "Between 1866 and 1948, top-flight African American clubs played over 7,000 games with White semi-pro, college, minor league, and major league teams and beat them nearly 65 percent of the time....From the first year of the American League in 1900 through the last year of the second Negro National League in 1948, African American teams posted a record of 316-283-21 (.527) against White major league clubs and big-league All-Star aggregations. Against intact National, American, and Federal League teams, black squads posted a record of 47-60-8 (.443) However, from the inception of the Negro National League in 1920 through 1924, African American teams went 29-31-2 (.484) in head-to-head competition. Because the White mainstream press was often reluctant to print Black clubs’ successes, the Negro Leaguers’ overall tally is likely far better than what was recorded."
"n 1922, responding to the Black teams’ continued success against American and National League squads, Commissioner of Baseball Kenesaw Mountain Landis forbade big leaguers from appearing as under their team names or wearing their own uniforms, and insisted that they advertise themselves as All-Star teams, with only three individual teammates allowed to play together at any one time. Between 1900 and 1948, Black clubs defeated the best White batters, pitchers, and teams they were allowed to play nearly 55 percent of the time. The All-Star squads included in this tally were composed of five or more players with big league experience (including the starting pitcher) and at least three players who had appeared in the majors that particular season. The number of big leaguers involved in many of these games was actually higher as the major leaguers often resorted to the use of aliases to avoid detection. As for the farfetched notion that the big leaguers were not giving their all, it should be noted that between 1900 and 1948, White major league squads racked up a record of 2640-897-71 (.742) against minor league, semi-pro, college and military teams—Only the Negro Leaguers had their number"
"While Negro League teams more than held their own while playing major league squads, they absolutely dominated bush leaguers. From the turn of the twentieth century through 1948, Blackball clubs played well over 1400 games with minor league teams and All-Star outfits, beating them nearly 60 percent of the time."