There is some confusion about the word 'header'. A html page has a part called 'head' or 'document head' where instructions for the browsers are tucked away, things that are not supposed to be seen on the actual page.
Then there is the page 'headline', the text that is indeed to be visible on the page. That is the one that needs to be styled as h1. The visible headline is NOT a part of the 'document head', but of the 'document body', or just 'body'. And to make it even more quirky, in html the part of the 'body' where the 'headline' is supposed to be, is defined as 'header'.
I have noticed many times here and in other connections where website building is concerned, that people use 'head', 'header' or 'heading' inaccurately. Maybe we ought to get our acts together and use the words correctly. I would sum it up like this:
head - invisible part of a html document with browser and search engine instructions
header - a location in the 'body' of the document where the 'headline', and maybe a banner or some graphics are supposed to display, at the top of a web page.
heading - the actual visible headline.