For some dogs crossing that invisible fence is a "cost" of roaming. They will stand at the boundary, hesitate for a moment, than charge through.

When I was a boy we didn't have an invisible fence, but the dog knew exactly where the property line was. The dog would stand at the line, contemplate the costs (punishment on return) and benefits, then bolt. There was a butcher shop a few blocks away. She would go to their back door and beg. A hand would extend out the door and drop scraps for her. Eventually, she would return (fat and happy), but go to the garage door knowing that her punishment was being banned to the garage for a while.

By the way in my post above, I meant to say "... in my area this is not an exclusively human male activity".