Actually there are two links in the post (#3). Hard to tell which one makes a better argument for Hebrew.
What they do show is that Lindsey and a handful of others who want the vernacular of 1st century Judaea to have been Hebrew are willing to twist any fact to fit their thesis.
Of course Paul knew Hebrew - as he said repeatedly, he was an elite student of the rabbinical schools.
Every Jewish scholar of the Middle Ages had a deep knowledge of Hebrew as well, but they didn't speak Hebrew as their vernacular either.
Paul's native tongue was Greek.
Of course the New Testament has plenty of Greek written with extensive structural similarities to Hebrew syntax - because Aramaic has an almost identical syntactical structure to Hebrew and Judaeans who spoke Greek as a second language imported Aramaic sentence structure into their Greek.
When Jesus is quoted in the New Testament in His vernacular, He speaks Aramaic: "Talitha cumi", "Eli Eli lama sabachthani" - the last phrase being a direct translation into Aramaic of the Hebrew Psalm.
If everyone in Jerusalem was so fluent in Hebrew, why did He speak the words of Scripture in Aramaic translation?
No, Dave W, there is zero evidence that Hebrew was the vernacular of 1st century Jerusalem.