>there are non-regular languages that pass the pumping lemma test
Can you give an example of that? You may be right, but I'm having a hard time coming up with a language that is not regular but fulfils the pumping lemma.
Sure, there’s an example in the Wikipedia article linked from the footnote in my comment above: the language consisting of all strings over the alphabet {0,1,2,3} with a substring of length 3 including a duplicate character, as well as all strings over this alphabet where precisely 1/7 of the string's characters are 3's.
As you can see, this example is a little complicated – and I don’t know a simpler one, so I’m not surprised you struggled to just come up with an example off the top of your head.
Can you give an example of that? You may be right, but I'm having a hard time coming up with a language that is not regular but fulfils the pumping lemma.