Usually, the colloquial conflation of Markdown with CommonMark and the numerous Markdown-esque dialects is helpful language, I've defended it here before.
On this question, it isn't.
Markdown qua Markdown, unambiguously supports HTML tags. You can verify that yourself: https://daringfireball.net/projects/markdown/
The introduction being:
> Markdown is a text-to-HTML conversion tool for web writers. Markdown allows you to write using an easy-to-read, easy-to-write plain text format, then convert it to structurally valid XHTML (or HTML).
It's not possible to read the original specification without agreeing that, yes, Markdown is specifically a way to generate HTML. It also has a nice syntax which has become popular in contexts where embedding HTML isn't a good idea, and there are some tools which allow Markdown to be converted to other formats as well (usually, but not always, these disallow most HTML tags, meaning that they aren't Markdown sensu stricto either).
I would say that all of this supports Hillel's basic point here: Markdown is in fact tied to HTML semantics, in a way which makes it painful to do things with it which aren't tied to those semantics in the same way. Dialects in the Markdown family exist which make this less painful, and they do so by diverging from the original Markdown spec.