Where does Space begin?
Blue Origins tweet is being a bit disingenuous there.
There is no Internationally recognised standard of where space begins.
The Kármán line was originally set by Hungarian physicist Theodore von Kármán in the 1900's at about 80km/50 miles. This was later arbitrarily reset to 100km mainly because it's a nice round number.
The FIA says 100km (though recently they considered putting it back to its original 80km).
NASA Mission Control (unlike NASA itself) considers it to be 122km/76 miles.
There is even a case for 1000km/600 miles as then the Earths atmosphere can be disregarded for all practical purposes.
The FAA, NASA, USAF, NOAA all think it's 80km/50 miles, and anyone going over 50 miles high as having been in Space and being an Astronaut. Even "real" Astronauts are surprisingly cool with this. Terry Verts (former commander of the International Space Station) and Mike Massimino both reckon that they are, with Massimino saying “I think if you get above that line, you certainly qualify as an astronaut, absolutely. The more the merrier!”, though let's face it, Mike Massimino is fucking cool anyway.
It brings up interesting political and legal questions too.
There is "Freedom of Space" at the moment, like "Freedom of the Seas" (much under attack now), where no one should interfere with your passage, or require permission or authorisation to visit or use.
If the limit on where Space starts was legally set and Internationally recognised, it would determine where that "Freedom" starts. Any object below that would be in your airspace when overflying you, and if you hadn't given permission or authorisation for it to be there, you'd be entitled to shoot it down if you had the capability.