The whole Is-Tackle-A-Rider-Or-Not thing is pretty goofy anyway, because it's blindingly obvious that she is. For dramatic purposes of the story, Hirayama said he wanted Tackle to be buried "as Shigeru's friend above all" and Muraeda has his Spirts version, and those are fine... in the context of Stronger and the classic Riders. Being a Rider back then sucked, it makes sense that you'd want to remember a fallen one as the person behind the mask. And Tackle didn't need to be called "Kamen Rider" to be a hero, that's basically the point of the character.
The problem is that explanation doesn't really hold together outside of context, especially after years and years of Tackle just being lumped in with the Riders by books (and these are things sanctioned by Toei) in an age where everybody gets to be a Rider. Hell, she has even been called "Kamen Rider Tackle" in some older books from when the show was on.
I mean, let's be real: if Arc, an oversized douchebag who doesn't even touch a motorcycle can be a Rider, Tackle can be too, if just not in name. Like Another Agito. Nobody seems to have a problem with him being a Rider, even though his name is not "Kamen Rider Another Agito".
I dunno. To me, Tackle will always be a Rider, even if they never call her one. Simple as that.