Truth Claims and the Poetry Difference in Wisdom Literature

I've been critical of Psalm 14 and Psalm 137 recently. One criticism of me is that I'm ignoring that these Psalms are not prose but poetry. I know the difference, but one thing that cannot be said is that poetry does not contain truth claims. Here's an example said by me recently to Brad Haggard:
Roses are red,
Violets are blue,
You are an idiot,
Jim West is too.
Poetry eh? Doesn't have any truth claims, eh?

Okay, I guess.