I know that a couple of UChicago professors told me that, especially if a graduate student ends up co-advised with two professors. Maybe there's an additional factor too: maybe students actually have the time and flexibility to communicate with other professors, which could possibly help initiate collaborations between them?
It happens, but rarely through co-advising. In my experience, co-advisors usually know each other before the student enters the picture, and the student has little effect on how much the faculty collaborate.
More often, students create new connections by becoming active independent researchers and working with a diverse set of collaborators. The various actors' roles as "student" and "professor" are simply irrelevant.
(I'm speaking for theoretical computer science, where PhD students are expected to become full-fledged independent researchers before they graduate. Your mileage may vary.)
In my experience, this is not the case. I was co-advised by a professor from another university, but no collaborations resulted from this. You could probably facilitate such collaborations if you really wanted to and put in lots of work though.
In my experience, getting a grad student or postdoc involved is often the best way to kick off a collaboration between two busy PIs (primary investigators). For any researcher with a large lab, their attention is often divided between many ongoing projects. A new collaboration often requires a significant investment of time and energy that may simply not be practical.
In this case, getting a grad student or postdoc involved can be good for everybody. The junior researcher can invest a lot of time and energy, receiving advice from both PIs, and see if the proposed collaboration is productive. If it doesn't work out, it's no worse than trying out a non-collaborative idea that doesn't work. If it does work, then the collaboration expands, benefiting both PIs. The junior researcher benefits even more, as they are now at the center of a growing new cross-disciplinary venture that clearly differentiates their work from both of the PIs involved.
Whether this involves formal co-advising or not is less important and a situational choice. Certainly, no such decision should be made until it is already clear that the collaboration is being productive and successful.
Things are different when you've got professors who have few graduate students and have more time to invest directly in collaborations, e.g., a professor at a primarily undergraduate institution who is still expected to continue doing research. In that case, the professor is likely to have more time available and should probably invest themselves.