Wow, that's a very interesting find, and does indeed show that the logos are indeed saved to the hard drive.
I think most of us had thought that the logo is stored on the server, and in order to have it verified and accessed, we need to be online. But I think your experiment shows that the logos are stored on the console hard drive but only accessible once it's been uploaded to the EA authorization server and verified.
There is some good news in your experiment. If the logo had been stored on the Team Builder server, and the site crash and every team was lost, you would still have the logos, if you had downloaded the team previously. So, after downloading, our teams' logos depend entirely on the Authorization server.