That is just patently false. If the honeycombs were circular, they would be rounded at the edges, and they would be different sizes, with gaps in between the cells towards the edges. Honeybees also don't have the building materials to exert enough pressure on the honeycombs to get them to change shape from a circle (see how difficult it is to squeeze straws like in your example, now imagine bees trying to do that. They don't have that kind of time on their hands).

In addition, it takes 8 ounces of honey to produce 1 ounce of wax, the bees would not waste wax by building circles, which would leave gaps until they finished the hive.

Biggest piece of evidence that they build hexagons, not separate cylinders: the hexagons share one wall, they do not have 2 walls that join together (there's no seam between the hexagons). They just build hexagons, building off of the ones which have already been completed.

TL;DR your friend the "beekeeper" is wrong. There's a Ted-Ed video that explains it really well in about 4 minutes.