I am an assistant professor, looking for the right PhD candidate: is it ok to contact a professor who is not listed in the references?
I don't know about HR standards for PhD candidates versus faculty positions. However, I have chaired faculty search committees and the general practice for equal opportunity hiring is that you treat all of the candidates the same. So, going above and beyond for one candidate over the others could be viewed as unfair.

If that is not really an issue for you in this case, I agree with The Fire Guy's comment that the student has a reason for not including this professor as a reference. Since you do not know this professor personally, there could be a number of issues at the workplace that could lead to an unfair assessment of the candidate. Although it could be that the candidate hasn't worked with that professor long, like you suspect, it could also be that there are personality differences between the two or the professor may be an unreasonable supervisor. Also, the candidate might feel that their applying to work with you may cause problems at their current position, if this professor knows about it. If you feel that the professor's feedback is important, you could ask the candidate if he or she is okay with you contacting the professor before hand. 

When I have applied for jobs, I would have been put off if I learned that the employer was contacting people who were not on my reference list. How would the candidate know that this professor is the only one you contacted?