First, it should be noted that all FL Scrub-Jays are not so tame. The further you get away from human population centers the less tame they are. I have been way back in the brush where the scrub jay is very cautious and absolutely will not come close to you. They more-or-less ignore you.
For areas where there is regular human traffic you will see scrub-jays behave more tamely. They are used to seeing humans on a regular basis. If it is an area where humans regularly feed them, they are very tame and in some very popular parks they can even become aggressive.
In most every group of jays there are a few that will not get too close to a human. They have decided early on that it may just be too risky. This makes me believe it is an evolutionary trait. But first let me get to the real reason why I believe scrub-jays are so comfortable around humankind.
These jays have evolved to rule small territories. And they stick mostly to the ground and low growing shrub or bush. They are masters of this domain. Since they spend so much time at six feet or below, they spend a lot of time around other creatures including humans. Though, we are relatively new to their environment when you consider they have been roaming North America for 2 million years and we have been here for only between 20,000-40,000 years. Simply put the scrub-jays we see today are descendants of jays that have been living near or around humans for thousands of years.
The evolutionary trait I mentioned a few paragraphs ago, I believe, insures the survival of the group should a human or other animal turn violent. It wouldn’t make sense for the entire family group to allow themselves to be exposed to a large and potentially dangerous creature.