Meet with another professor in our university to discuss a paper that I wrote and her student is co-author with me
It is typical for advisors to want to help emerging PhD students in their efforts to publish papers. Typically, advisors can give a paper a rudimentary review with little time or effort. You would typically recognize this support with an acknowledgement, not coauthorship (in the fields that I am familiar with).

This seems to be in line with what your coauthor's advisor has in mind. I would take the coauthor at their word regarding the fact that the advisor does not wish to be a coauthor. 

In addition, you do not want your own advisor to be in the dark about this paper. It is good that you have presented it to him at a prior occasion. Prior to meeting with the coauthor's advisor, you should email your advisor about the paper and let him know you are preparing to submit it. Depending on schedule/your needs, your advisor will likely be willing to provide a brief review of the paper. If he does, he should also be expecting an acknowledgement, not coauthorship.