I actually tried to decline a recent rank, because I did not feel deserving, and there was NO disrespect intended or taken from my sensei.
We are a very small group, and been going through some serious growing pains as well as personal issues that have limited regular practice. For example, during this time, we lost our training venue and had to find a new place to train. That said, simply having everyone show up and test at our new venue was an accomplishment. Our sensei, looking at the circumstances and our testing, believed we each had learned enough to advance one step (not a full rank).
I discussed this privately with one of the upper ranked students, who was also one of the judges at the test and one of our regular teachers. I told her that I did not think my performance was worthy of any advancement, because I had maintained skills, but not advanced. She disagreed and pointed out several new things I had learned and improvements on my technique. She did, however, agree that my technique would not normally be worthy of advancement. But, she also advised me that perhaps my sensei saw my dedication (I trained into 8th month of pregnancy, although much modified), spirit, and determination along with my advancement in knowledge and skill earned me a rank that I would "grow into" quickly enough.
So, I let my sensei know that while I did not feel deserving of the rank, I would do my best to honor it and be worthy of it and advancement at our next testing. I still do not think I was worthy of the rank awarded, at the time I was given the rank, but it has made me work harder to feel worthy of it.
So, I would offer that declining rank is not always a matter of disrepect or "I know better". For me, rank is not to impress anyone else, it's an internal measure of how far I've come and the honour given to me by my instructor and peers. I believe that declining rank should be looked at on a case by case basis. Sometimes, circumstances (be they financial or otherwise) may call for it. I also think this is something to be discussed privately between student and teacher.