Jennings was terrible as a Colt. Coaching or not. Fans don't really care - if you repeatedly stink it up, you are going to get reamed.....I'd suggest a Pro-Bowl calibre player would be able to work with a coach to improve his play, if it really was down to poor coaching.
And I don't really care why some fans ream a player. Just like I really don't care about some of the current fans who bash Luck for his poor completion percentage and high number of INT's. I understand, like many do, that Luck's low completion percentage and high INT's come from the type of offense BA is running and a very poor OL. That's not to say that Luck is perfect...there are things he needs to work on, but a lot of the things that some people are complaining about aren't entirely his fault. However, it's the responsibility of the coaching staff to help Luck fix the things that are his fault.
I wasn't really a fan of Jennings either while he was here because he did play poorly. However in hindsight, and seeing how he's playing in Chicago, I think it's more than fair to say that his poor play was the result of either poor coaching, poor scheming and/or being pushed into a system that didn't play to his strengths.
I also find the latter half of your post to be pretty ridiculous. It's not the player's responsibility to work on improving a poor coaching staff. It's the coaching staff's responsibility to coach and develop a player, and if the coaching staff isn't capable of doing that then it's up to the HC and/or GM to make changes to bring in a coaching staff that can help develop players. Especially when you're talking about a late 2nd round pick like Jennings was. If he were an instant pro-bowl caliber player then he would have been a top 5-10 pick in the draft, don't you think? Since that was not the case, he clearly was not pro-bowl caliber upon entering the league, and therefore it's up to the coaching staff to develop him and bring out his full potential. Otherwise, what's the point of having an entire coaching staff? The previous regime's coaching staff could not, in 4 years, help Jennings to realize his pro-bowl caliber potential, but the Bears' coaching staff has been able to.
They say you can catch more flies with honey than you can with vinegar, but does anyone know what the final tally was? And why didn't they try manure? And if they did, how would that have changed the saying? Would it be, "you can catch more flies with honey than you can with vinegar, but you'll catch the most if you're full of crap?"