I have read on several websites that using the link element is not beneficial/necessary if the favicon is already stored in the root directory of the domain under the name "favicon.ico". However, if the file suffix, name or directory path differs, the link elements will be crucial.
Did I understand it right?
Exactly. The favicon in root and no link is the approach used by Google itself. But there are cases where you cannot place the icon in the root directory or you don't want to pollute this special directory. In that case, a link markup is necessary.