You're not this naive or easily misled, are you?
I have a 13 year old son who attends the local middle school. If asked the following question I could easily answer no: "Gazoo, does your son attend the local middle school?" "No."
What?? I could pass that test with flying colors. I don't KNOW he attends there. I know our house is district-ed to that school. I know he brings home report cards. I know his friends have never told me he skips school. But I have never personally attended a day of school with him, so I do not KNOW he attends.
Likewise, Pitino didn't personally participate in paying Bowen's family or know with certainty that he was paid. Plausible deniability. And for $10K there's a guy who will teach you exactly how to pass a polygraph test and he claims to have a 100% success rate (and has been sentenced to jail for it but won't stop doing it).