In my industry, company ABC invented "widgets". They are a monopoly multi-national company, is the Authority in our industry, have the most traffic, most backlinks by far and plenty from .gov, .edu and major publications and from authority authors, have tons of anchor text related to their main keyword, have the most social signals by far. Have huge resources and content.
They also have a in-house web and SEO team
Yet for "widgets", they are not no 1, they have been around position 4 and 5 for an internal page for a year or so now. There homepage is way back in the SERPS..