I was able to find a few elements that are able to make this connection possible. I'm guessing the designer used some type of bar-sized element which is made from a different material that is able to compress slightly more than regular ABS. For example, the softer plastic used on some minifig weapons seems to work nicely:
Another option could be flexible Technic tubing. I was able to make this work, but it feels like a very tight fit. This tubing could also be cut to length under some definition of LEGO purism.
Of course, as Kramii pointed out, this could also just use non-standard elements or part modification.