100 million unique players of the game (and last I checked this number had been revised down to 80-90 million) per month. 0.006% of that would in fact be 6,000 - but that is 6,000 unique individuals. That does not include smurf accounts of individuals who were previously permanently banned - remember, this is talking about humans, not accounts.
Riot has consistently responded confirming that those statistics have not changed recently (back when they spent the time to respond to this sort of baseless complaint with no evidence) - and given the rate of change of players (consistently increasing) it seems plausible if not certain that the percentage hasn't changed.
For example, if a game has 100 players and 1 gets banned, there's a 1% ban rate. If the game then increases to 100,000 players, and there's 1,000 banned, that's still a 1% ban rate - but compared to the original there's 1,000 times as many banned players. More banned accounts in number does not translate to more banned human players in number.. which does not translate to a higher percentage.
TLDR: There's absolutely no reason to distrust the statistic at all.
