Absolutely not. if people are publishing sports of cultivars under that same cultivar name, I'm sorry, but these people don't seem to understand the whole purpose of cultivar naming: it is to differentiate that plant from others.
Some cultivars in other species can have different color flowers, for instance, and that would be evident in the individual cultivar description. But that doesn't happen with AVs, as they are always propagated with asexual material (not seeds). New plants are exact copies of the mother plant. If they are not, as in the case of a sport, they are no longer that cultivar.
What a mess things would be if they were, since, for example, practically all AVs in the world (excluding in the wild) are descendants of ten or so original hybrids. Conservatively, a quarter of those are sports. Should we regress and change the names of the those 4,000 (out of 16,000 cultivars) back to the original ten?
Even with a caption explaining it is a sport, it still should not be placed under the parent cultivar. Very few viewers actually read captions or delve deeper than a pretty picture or gotchya headline, and this is how pseudo-facts are spread throughout the internet and social media.
This is my opinion, because I have been chastised multiple times for pointing out inherent inaccuracies in the database here that constantly reoccur. The administration here, weighs the "fun" of the database against the importance of accuracy, and makes a decision. So if you want the real answer, you better ask them.