Being able to verify certainly makes it easier, but a standard like "Ensure all images have alt-text" does not require a screen reader to verify.
And the thing with standards is that often no existing product (screen readers in this case) will fully comply with the standard - so if a given screen reader fails on your site, it may well not be your site's problem. This was (and perhaps still is) the case with Web standards in general. In the old days, there was usually not a single web browser that was fully compliant.