Hey Casey, this is one of the areas where things get a little weird because the W3 doesn’t actually have any say over the ADA guidelines, it is more than the ADA guidelines adopted the WCAG 2.0 guidelines as just that, a guideline to help. As far as I know, the tool you’ve linked to hasn’t been used in any judgements I’m aware of. Usually when it comes down to making a decision on if something is/isn’t compliant they have people use the actual PAWS tools and show what elements do/don’t work as intended or are otherwise inaccessible. Hope this helps!

The Americans with Disabilities Act (ADA) was first passed in 1990. Twenty years later, the US Department of Justice released an update called the 2010 ADA Standards for Accessible Design. These standards cover the design of physical spaces and have been interpreted to include web locations as well, so it can be difficult for the would-be accessible website designer to use them.
Through the Americans with Disabilities Act (ADA), our nation committed itself to eliminating discrimination against people with disabilities. The U.S. Department of Justice’s (DOJ) Civil Rights Division is proud to play a critical role in enforcing the ADA, working towards a future in which all the doors are open to equality of opportunity, full participation, independent living, integration and economic self-sufficiency for persons with disabilities.
Upon discovering issues faced by disabled government employees and the public, revisions to section 508 were made. The issues that were uncovered involved websites, documents, and software programs. As of January 2018, the updated 508 standards require all federal agencies and contractors to create web content accessible to all. The updated standards also include Website 508 compliance.
The U.S. Department of Health and Human Services (HHS) also enforces Title II of the ADA relating to access to programs, services and activities receiving HHS federal financial assistance. This includes ensuring that people who are deaf or hard-of-hearing have access to sign language interpreters and other auxiliary aids in hospitals and clinics when needed for effective communication.
Again using the WAVE toolbar, check for Errors, Features, and Alerts. If there are many errors, I assume this page will not serve as a good example, and stop checking. If there are only a few errors (e.g., fewer than five) I'll check those errors and might be forgiving if they're relatively minor and are offset by good accessibility in other areas.

Covered entities are required to provide aids and services unless doing so would result in an “undue burden,” which is defined as significant difficulty or expense. If a particular aid or service would result in an undue burden, the entity must provide another effective aid or service, if possible, that would not result in an undue burden. Determining what constitutes an undue burden will vary from entity to entity and sometimes from one year to the next. The impact of changing economic conditions on the resources available to an entity may also be taken into consideration in making this determination.
Accessibility on the web can mean a lot of things. But in general it means making websites as inclusive to as many users as possible. Accessibility is important for a diverse group of users including mobile users, people who rely on assistive technology to navigate the web, and even search engine robots. We handle accessibility of WordPress.com in two simple ways.
Accessibility by UserWay UserWay creates a simpler and more accessible browsing experience for users with mobility issues. Millions of people cannot use a mouse or other pointing device and rely solely on their keyboard to navigate websites. Your site should be fully navigable using a keyboard’s tab key, arrow keys, the enter key and the space bar.
Another federal agency, the Architectural and Transportation Barriers Compliance Board (ATBCB), also known as the Access Board, issues guidelines to ensure that buildings, facilities and transit vehicles are accessible to people with disabilities. The Guidelines & Standards issued under the ADA and other laws establish design requirements for the construction and alteration of facilities. These standards apply to places of public accommodation, commercial facilities, and state and local government facilities.

This guidance document is not intended to be a final agency action, has no legally binding effect, and may be rescinded or modified in the Department's complete discretion, in accordance with applicable laws. The Department's guidance documents, including this guidance, do not establish legally enforceable responsibilities beyond what is required by the terms of the applicable statutes, regulations, or binding judicial precedent.