Yeah, there's a few causes for a 503, including the site being offline. However, the Error Check is just a quick check. There are some issues it can't find, and others it can erroneously report. While it's very helpful, it's not perfect.
If the front-end of your site works to you and you don't see any issues, I wouldn't worry about the problem. If you do run into issues though, definitely let us know and we can help you look into it further.
Thanks,
Alex