I think the one knock on him being truly, truly great, is aside from the last title (where a healthy Perk likely would have changed the outcome), Kobe was never even clearly the best player on those championship teams.
Granted, that is partly a testament to Shaq's greatness, which isn't Kobe's fault. But was there ever any question with likes of MJ, Larry, Chamberlain, etc. who the best player on the team was? And even if that isn't a direct knock on Kobe, I think that fact that the bulk of his success came with Shaq does diminish his accomplishments. How many titles would even someone like PP have won had you put him next to Shaq in his prime?