I attempted to mirror what you outlines. I used the text editor to add text to a page and also the link to https://www.googles.com. The Broken link checker detected the broken link. I edited the URL to be https://www.google.com and had it recheck the link, the Broken link checker confirmed that the link was now working. However, the actual page link did not change. It still links to https://www.googles.com