Should I accept the counter-offer if my reasons for leaving are resolved by the offer? ?

I was offered a job that I didn't truly believe that I would get because I don't quite have the education (still a student) and experience for. The position is staff accountant. I currently work as accounts payable. I accepted the job because it's what I want to do, what I am going to school for and am working towards. I also did not believe I could get this position at my current company since they already have one staff accountant and no apparent need for another. When I gave my resignation and explained why I was leaving I was offered a job counter offer in which I would get promoted into staff accountant and they matched the pay increase and went above quite a bit. They said they had planned on adding the position later on and giving it to me but would give it to me now in order to keep from leaving. I was excited about it at first because I like the people I work with and the company is a pretty good company. It seemed like this was the answer to my problem which is that I don't want to work accounts payable anymore. However I have just finished reading a wealth of information on the internet about how counter offers are the devil and accepting one is career suicide. I trust my bosses and I don't believe they would lie to me however I am now uncertain as to how this will affect our working relationship not to mention that of my coworkers. I honestly did not expect this and was on cloud nine at the thought of the new job. Now what? Opinions please. Does anyone have a counter offer acceptance with a happy ending?