To get a feel for this situation from the student's point of view, I suggest reading questions such as Changing PhD programs: should I submit a recommendation letter from my old advisor if it's not purely positive?, Incompatibility with the PhD advisor, Switch PhD program: how to contact possible PhD advisors when already enrolled in PhD program?, and many others.
The decision to try to switch programs is a difficult one for the student. They may be worried about harming their relationship with the current advisor if the move does not work out. From this point of view, contacting the advisor, rather than the student, would be like calling a job applicant's current employer.
Although if they asked here they would probably be advised against it, there may be a temptation to just not mention the current PhD program other than to the extent that they have worked as a research assistant.