Um...the header only disappears for me on any of those sites when you scroll down - which is pretty much what you'd expect. There is a very short span on the military.com one where it disappears/reappears - but it's a pretty short blip. And the ad goes away entirely. I dunno - it's a bit odd. The foxzero.com site just loses the site name - and that actually looks more like an error in the code to me, than an attempt to do anything fancy. The others don't do any reappearing after I scroll down.
As for hamburger menus - unless you want to use a boatload of space to get all your nav links on the page - dropping your content well "below the fold" - then yeah, you need a menu that opens when tapped. Teeny, tiny text links don't work with big fat fingers.
My beef is people who now think they're being clever by using hamburger menus everywhere - including the version for computer browsers. That, to me, makes a site LESS usable - forcing the user to click around, rather than laying out at least the basic navigation so the user has some clue what the site offers. If you've got screen real estate, use it effectively! Of course, the mobile use of websites is only increasing; not designing for it is now a cardinal sin (or just plain stupid).
