The selection of a speaker stand must fulfil only two core criteria: raising the tweeter so that, ideally, the tweeter is level with your ear (very few users do this and hence very few users achieve the full sonic potential) and protecting the speaker from toppling over. With those criteria met, there is a very wide latitude on materials, shape size and colour.
This is ludicrous assertion by Shaw. How a speaker stand interacts with the floor can, depending on other variables, produce clearly audible differences.
The quote is reminiscent of when, years ago, Shaw was famously agnostic about amplifiers:
Whatever amp you've got will work just great with Harbeth. Anything British, made after about 1980, fully serviced will be great. End of story.
Shaw designs excellent speakers, but at least some of his related views should be taken with a large grain of salt.