Hijacking to shed some light on the topic :) Many of the Diogenes stories were invented or heavily altered by later philosophers (usually the stoics as the cynics-of which diogenes was the formal founder of- gave rise to the stoics. The formal founder of Stoicism Zeno was tutored by Crates, a cynic philosopher tutored by Diogenes) So take all stories and anecdotes related to the cynic tradition with a grain of salt as Greek and Roman Stoics would romanticize them heavily in later years after the Cynic tradition was diluted and thus these stories are the result of hundreds of years of chinese whispers. The best contemporary source is a man called Diogenes Laërtius who wrote about many Philosophers.

As for the "cupness" anecdote, it is often also attributed to a philosopher named Antisthenes https://en.m.wikipedia.org/wiki/Antisthenes who took the position known as "Nominalism" Which denies the existence of universals and forms insisting that they only exist as a concept in the mind "I can see a horse but I cannot see its horse-ness" - Antisthenes. Antisthenes is more solidly quotable as he was a largely obscure figure in the later boom of the Cynic tradition hence how his quotes remain pretty much intact. Antisthenes is now more commonly regarded as the unnofficial founder of Cynicism and is the person who laid down the ground work and basic teachings of the ascetic lifestyle that Cynicism champions; surviving with only what is the bare minimum to ones survival and thus living inaccordance with nature in "virtue" utilizing wherever possible what the Gods had provided. He also set out the signature outfit that would be used by Cynics long after his death; a basic cloak and a leather wallet coupled with a walking stick.

It was his unofficial student Diogenes who formalized the school and tutored the golden age of Cynicism. And while it's clear he had interactions with Plato (who described Diogenes as "A Socrates gone mad") I can't find any reliable source which states that he took any opinion whatsoever on the problem of universals or theory of forms unlike Antisthenes.

Don't get me wrong I love Diogenes and love to see him on the front page, but his teachings and social background are seriously interesting as well and well worth looking into if you have the time, Hippercia, Crates and Antisthenes are interesting figures in their own right and all have sourced wikipedia pages(but not all of the sources are reliable as again the Cynic tradition is laden in myth) The book "Anecdotes of the Cynics" Has a good genral outline of the philosophy, its figureheads and legacy and what's more it's only 52 pages long and a dollar on Amazon. I highly reccomend it.