There has to be some correlation. How many players have terrible seasons as Jays and then get traded and turn into solid contributors? I know it's a small sample size with Boni, but he's never been as bad as he was as a Jay, and he gets traded and has a good run like this? Dickey wins the Cy Young last year, gets traded to Toronto and suddenly has a 4.00+ ERA? I could go on...
A lot of the responsibility falls on the players themselves, but obviously coaching has an impact on the game. Otherwise we wouldn't have coaches.