This is a similar but not the exact answer.
From my recent web search result, I happened to visit this page: Recycling & Waste Minimization by Office of Sustainability, The University of Illinois at Chicago (UIC). Their recycling approach had some resemblance of what have been described the question. I have noted the following points.
Point 1. Item example is "Styrofoam" (may be a coincidence)
The following text have been quoted from above link, which included the anchor link tab "How Recycling Works at UIC".
START WITH SMART MATERIALS
It begins when the materials available for use on campus are chosen based on compatibility within our recycling program. If an item (for example, Styrofoam cups) is provided for use on campus, it is everyone’s responsibility to ask why it was chosen in the first place. Watch how Joe Iosbaker, UIC Recycling Coordinator, explains the recycling system in this short video.
Point 2. Links to a video on YouTube
"This short video" is linked to a video on YouTube. The video has length of 3:46 minutes and the description has been quoted at below:
UIC Recycling Program Basics
UIC Office of Sustainability
Published on Feb 16, 2012
Joe Iosbaker, UIC Recycling Assistant, goes over how the UIC Recycling Program works. Recorded and edited by Andre Thomas, UIC Office of Sustainability Media Intern, Fall 2011.
Point 3. Have bins at central point i.e. "Hallway Recycling"
There is an inline image under the quoted text. I have captured the top-half of the image and transcribed relevant text from the image.
Desk-Side Recycling - Place all recyclable materials in the small blue bin by your desk.
Hallway Recycling - If you don't have a desk-side bin, or when the bin is full, sort the materials in the hallway stations. We all have a responsibility to properly recycle at UIC.
Nonetheless, UIC is an English speaking university.
Despite the resemblance, there are few missing points:
No mention of "no longer put trash cans in each individual office" (However "Desk-Side Recycling" seems to be not necessary, as hinted by description text for "Hallway Recycling").
No mention of "good reasons" why the approach was established as such at their university (They only explain how their approach works).
No mention of "needed to recycle styrofoam and such" (Besides the brief mention of "Styrofoam cups" as example and other solid waste such as food scraps collected at their dining halls; bottles and cans).
No mention of "different people were interviewed" (There is only one person who explain the recycling steps in the video).
After all, this answer might not be the one that OP was looking for.
I wish there were more reliable clues in the question to figure out how they managed to remove trash cans from the office at all. Based on the broad clues of "English speaking university" and "no trash cans", I can guess of only one place: Singapore. Although, I only heard that Singapore provides no trash cans in public area and not aware of waste management inside the buildings.