Summary required for complex tables?

Some are interpreting the guidance on the W3C Web Accessibility Tutorial
that a summary is required to meet WCAG for *complex* data tables.  Is that
the intent?
In other words, should a checker, if it can detect a table is complex,
check for a summary?

The confusion is with the phrasing "is usually only needed" as meaning
"required".
Is it always required for complex tables, or only sometimes, and so could
be a AAA Success Criteria?
Either way, the WCAG 2.1 spec, Tutorial, techniques, and Understanding
should be more explicit, hence I'm copying the editors.

https://www.w3.org/WAI/tutorials/tables/caption-summary/
"... A summary is usually only needed for complex tables."

Understanding 1.3.1 Info and Relationships is mute on the subject of
complex tables.
https://www.w3.org/WAI/WCAG21/Understanding/info-and-relationships.html

Techniques listed do not address summary for complex data tables
https://www.w3.org/WAI/WCAG21/quickref/?showtechniques=131#info-and-relationships

p.s. I'm not talking about 'summary' that was deprecated in HTML 5.
 ___________
Regards,
Phill Jenkins
See the new IBM Equal Access toolkit and accessibility checker at
www.ibm.com/able
pjenkins@us.ibm.com
Accessibility Executive
IBM Accessibility
linkedin.com/in/philljenkins/
www.ibm.com/able
ageandability.com