This is the subject of a major halachik debate, you definitely shouldn't go around calling speaking that way about them.
That being said, you definitely shouldn't assume something fits your standards because the website has the word kosher in it.
There are a few heimish wine stores in brooklyn that sell non-kosher fyi. The rye you mentioned i believe its AYLOR
I know that heimish stores sell it and others in the category of companies owned and operated by jews who specifically don't sell their chometz. That does not mean they are permitted or that we are permitted to consume chametz shavar....
For those that do not know I am referring under the company sazarc or bufulo trace (besides the one that says KOSHER on it) which each include dozens of brands. I never herd of a any OR that permits this, can you please share the name of one?
PSA: not interested in a halachik debate just a name. DMs welcome.