When a URL is submitted to Google, we look for it in our next crawl. If you've already submitted your URL, your site could easily appear in our new index, which will go up when the current crawl is completed. However, if no other site links to yours, it may be difficult for our crawler to find you. Conversely, if many sites link to your page, there is a good chance we will find you without your submitting your URL.
So when they say they look for a submitted URL, it seems that they mean they hope to find it by following a link. So, perfectly good question, silly answer.