Okay to state very specific research interest in statement of purpose? *I am applying to Psychology PhD

For graduate (PhD) applications, most universities ask for a statement of purpose and instructions simply state to discuss your research interests. This type of open-ended prompt suggests to me that they may also be anticipating a rather wide range of research interests from the student. However, for my case, I actually have 2-3 research questions I intend to look at. I have also contacted a professor at the university, to which the professor responded that the questions were interesting and exciting to research. However, since the questions are very specific in nature, they do not correlate very well with many of the other professors' interests in that department. Only the professor with whom I have been in contact with has those topics listed as their areas of interest.

From a PhD admissions committee perspective, would a student who has clear ideas of what research questions they want to research be viewed positively (i.e. sees the student as being prepared) or negatively (e.g. student's lack of interests in other professors' labs), assuming GPA, GRE, etc. are adequate.

I thought about writing my specific questions but also state that I'm open to new ideas, but I was not sure whether that will come off as being snobby or, conversely, desperate.

Any advice from people who have read or written a statement of purpose would be greatly appreciated!
First, how about asking the opinion of the professor who has the common interest with yours?  S/he will hopefully be able to assess how much influence s/he might have with the admissions committee.

For the rest of my answer I will assume the professor advises you not to make your statement too narrow.

I suggest you start off rather broadly, for approximately one paragraph, talking about an area that includes at least one of your specific research questions.  At this point you are filming the city from a helicopter or drone.  In the next paragraph, you can bring your camera down to street level, and start describing one or more of your specific questions, as an example.

If you are really creative, you could write the broad paragraph in such a way that at least one other professor in the department could see some spark of commonality.