Accessibility is about much more than screen readers. If a user experiences problems accessing your site, that’s an accessibility problem, no matter what physical attributes that person possesses.
It seems you've been misinformed by the current generation of web designers. Accessibility is actually limited to people with disabilities, though a few people have started to use it interchangeably with usability. [0]
I agree with the spirit of your message though, but that's not what the grandparent post claimed.
> Accessibility is the design of products, devices, services, or environments for people with disabilities.[1] The concept of accessible design and practice of accessible development ensures both "direct access" (i.e. unassisted) and "indirect access" meaning compatibility with a person's assistive technology[2] (for example, computer screen readers).
There is more to accessibly than screen reader compatibility. (I want to emphasize this point, not because I think you said anything to contradict that but because I think that is a point lacking from the conversation in this thread)
For example, I'm autistic and use a "normal" browsers, but garish websites (for example those displaying animated ads) are less accessible to me, because those lead me to becoming overstimulated, making me less likely to absorb and remember information presented on the page as well as being physically and mentally exhausting.
I am perfectly willing to pay for content (and am, through Spotify, Netflix and Patreon), but much of the web is actively hostile to many disabled people. My physical disabilities don't prevent me from using my computer in the standard way but every time I misplace my mouse and try to navigate the web solely using keyboard (which isn't that far from how I usually use my computer, so it's not like I don't know the shortcuts) I am reminded how it must be for people who are unable to use a mouse and have to rely on other input methods. Many websites couldn't have worse UI when it comes to accessibility if they tried.
There's a wide spectrum of accessibility between "content as created by the designer" and screen readers. People with a vision impairment who do not require a screen reader can use the browser's built-in magnifying/zooming capability to make a site usable for them, but only if the content is visible.
The content is there, it's just hidden through css. If anything, a screen reader has access to the content earlier than the unimpaired people.