Lie? Oh, no, that would violate their own principles! ;-)
It's ironic how the BSA will complain that people are trying to destroy them with lawsuits when lawsuits is exactly how the BSA got started. I was just reading that there were many other boy scouts organizations, and one was called American Boy Scouts. BSA sued ABS to make ABS change its name; it did, to United States Boy Scouts. Then BSA petitioned for the congressional charter, and then it sued USBS to get it to stop using the name "boy scouts". One source said USBS changed its name again to American Cadets but then disappeared eventually. Meanwhile, the BSA proceeded to swallow-up the other boy scouts organizations in a more "friendly" manner. In 1989, the BSA reportedly "threatened" Wilderness Scouts with a suit, though I'm not sure what is meant by that. The Wilderness Scouts still exist - I forget which state they're in.
The Canadian brewers of "Moosehead Beer" are currently suing the American brewers of "Moose Drool" beer over the use of the name "Moose".
If you come up with a cola drink formula and use "Coke" in any part of the name, the Coca-Cola Company will be slapping you with a lawsuit 15 minutes after they first hear about it.
If you market little marhmallows under the name of "Microsofts", you will be hearing from Bill Gates' lawyers.
Organizations protect their name recognition with lawsuits. What's your point?
Just because Pepsi does not use "Coke" in any part of it's name does not stop them from putting out a cola product by another name. So it is with any youth organization as long as they leave out the name "Scouts".
For example: "Boy Pioneers"