A true tourniquet is designed to crush blood vessels and absolutely prevent the flow of blood. They should only be applied when a major artery has been severed, or if a limb has been removed, or severely mangled. They should not be used to staunch normal bleeding.
Many folks confuse the tourniquet with a constriction band, which is intended to stop most blood flow, but not crush vessels. It isn't semantics, there is a significant difference between the two. A tourniquet applied incorrectly can result in the loss of the limb or major tissue below it. It may not cause the loss, but it can. IN any case, it isn't BS in the least and is based on real-world experience. Times change, and modern "tourniquets" may be nothing more than tight constriction bands, but the warning isn't BS in the least.
Ash