I think the majority of people who say they agree with Popper read him like this:
Popper says there is no verification or justification. They think "That sounds stupid. I must have misread it. Let me try to find a better interpretation." (And, by the way, if they didn't know to do that in advance, they might well learn it while reading Popper, since he's a big advocate of seeking the best possible version of arguments one encounters.)
So, they try to think of a way to change Popper's statements about epistemology to be more reasonable. They end up interpreting his statements to be consistent with the only epistemology that makes any sense to them: the prevailing one.
And so they go through the whole book interpreting everything Popper says as advocating justificationism, induction, and the theory that knowledge is justified, true belief.
They perhaps take Popper to be making some critiques of it, for example they might notice Popper denies that infallible justifications are possible, but overall they take him to fundamentally agree with justificationism. What else could he be saying? As far as they can see, it's the only possible, conceivable approach to epistemology. One can't disagree with it; it's the manifest truth of how to think. Anyone who disagrees with it wouldn't be able to think; he'd end up in an insane asylum.
Let me emphasize: I think a majority of people who claim to agree with Popper do not. That's how hard communication and persuasion are, and how different two people who think they "agree" often are. Popper knew people are different and persuasion is hard, but I don't think he ever said it this strongly.
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