As for Dhoni's comments, the reason why they grate on me personally is that I didn't find them professional or constructive. What is constructive is to complain all you want about specific instances, demand resignations, etc. in the umpire's report at the end of the match which I'm sure Dhoni did. Doing that plus going to the media to rag on a fellow professional didn't sit well with me at all. That he didn't mention Harper by name is irrelevant, we all know who he meant. Plus, as has been alluded to already, it insults the WI team and belittles their efforts ("The match was only close because of the incompetant/biased umps!") and presents as a bit of an attitude toward an entitlement to the win.
Whether Dhoni meant any of that or not I don't know but it brings me to where I think things have changed for India. When a team goes from being a an also-ran to the top banana, people's perception of stuff you do and say changes and, especially where the press is concerned and you need to be mindful of it if you don't want absolutely everyone to hate you. Aussie players received media training once the team started winning regularly for this reason and even then still got it wrong plenty of times. If you complain about the umpiring when you win, that'll annoy a lot of people but people will really hate you if you do so as the overwhelming favourite, especially if you've sent a second-string side (insulting enough and was so when Australia did it). The general perception will likely be along the lines of "You won and were expected to. What more did you want? Stop bitching!" It's also galling for the BCCI to cite crowded scheduling for sending that second-string side for the obvious reasons.
I reckon the Indian heirarchy are still getting used to the enmity which people have for you if you're number 1 and if they want to change perceptions about them, they'll have to get savvy about it. Or they could, as the cricketing and financial powerhouse of the game, assume their position will last forever and they'll never need to...
Either way, what I'd have preferred Dhoni do is leave his complaints in the match report and to the media, say something like "Well, we won and that's what matters. Yes we had some decisions in the match which caused concern but we've made our feelings known about them in the appropriate forum, thanks for asking."