You've missed the point I'm afraid.

While people know that Android is based on Linux, a fact that isn't in question, when people say a "Linux" phone, they're not discounting that Android exists or that it runs Linux, they mean to infer that they're discussing non-Android Linux phones. If they meant Android as a Linux phone, they would have said Android.

While android is in the set of "Linux", not all things that are in the set of Linux are Android.

Since we have a specific word for GNU/Linux - Android devices, but almost all Linux based alternatives to Android for mobile devices is basically referred to simply as a "Linux phone", it can be, and should be, assumed that the speaker is referring to Linux phones which are not Android.

It's a nuance of language and technically not wrong to say that "Android is Linux" but that's not what most of the readers understood to be the speakers intention.

That was the correction that the previous poster tried to portray.

Simply put, most Linux enthusiasts and community, doesn't really consider android to be "one of them" since, though it's Linux at its core/kernel, almost everything built on top of it from there is some bastardized/closed source software, or relies on something closed source. Most of the things people want to run on their phone (browsers, camera software, even the dialer), is almost entirely written, controlled and closed source by Google. While some of the "guts" of the OS might be open source/GNU versions, the interfaces are largely all closed source software that Google has published to run on top of Android specifically. This doesn't fit with the philosophy of GNU/Linux, and therefore Android is largely not included when speaking about Linux, at least for Linux enthusiasts.