It does in fact have to do with the suppressor element, as it is the presence that 5th element that distinguishes the characteristics of a pentode (of any type) from otherwise that of a tetrode -- which (among other things) is all about the resulting characteristic of the knee.
In the technical manuals, only Sylvania uses the term "Beam" in its descriptor for the 6CA7, referring to it as a Beam Pentode. All other manufacturers refer to the 6CA7 as a Power Pentode. It is specifically Sylvania's "Fat Boy" version then that employs the beam topology (aligned grids and beam forming plates). GE manufactured the fat boy version as well for a period, while RCA simply sold relabeled Sylvania examples. The 6CA7 offerings from all other manufacturers remained true to the original EL34 pentode construction.
The significance of this is that the Sylvania fat boy was not the beginning (nor the end) of the 6CA7. The 6CA7 started life (and continues) as being the original Philips EL34 tube, but designated by the American numbering system. The Sylvania fat boy beam version then was simply just that: a unique version of the tube. While many have come to use the fat boy's beam topology to define the difference between the EL34 and the 6CA7, such is not the case. The 6CA7 existed -- as did its direct relationship to the EL34 -- well before the fat boy version was even an idea to be had. As a result, the beam characteristics of Sylvania's fat boy version distinguish it from both the EL34, and the 6CA7.
Dave