Absolutely, and debate is good because it helps every one understand better and become more knowledgeable professionals.
My understanding is that some LED lights are generically designed and therefore output a particularly 'standard' range of light frequency. In the same way, many LED gels are created from a base formula by one factory, and bought by many other companies that use it to make their own brands to package and sell, therefore meaning they can all be cured by the same output, as they are all essentially the same.
Others may be unique, but are still developed with properties that are able to cure without specific equipment., as long as the lamp you have outputs the frequency of light needed by the product.
On the other side, other companies deliberately manufacture their products to be completely different and have different properties- such as CND, which among other things was designed with different ingredients to be hypo-allergenic whereas others are not, and so as a consequence has a curing requirement much narrower than other products and the output of other lamps. This is why a lamp was specifically calibrated for the needs of Shellac, and other lamps very often won't cure it- their output in terms of light frequency doesn't match.
Companies that specify a specific light with have designed and tested not only for LED output, but also placement and angle of the light and other clever engineering ideas to accommodate the specific needs of their product compared to general formulas.
Does that make sense to you?