I agree with the first commenter on the link. This is quite a reach. It's unlikely that the order to take down an old, unmaintained site would have come from someone who's in on some sinister agenda to revise history.
It got emailed around or something, and someone who was close enough to a WH staffer or DNC person saw it, and send it along.
They asked their boss what to do, and the answer was "just change the website".
It's not like there was some ordered plan of "first we'll change this, then we'll change the transition site". It's clearly a reactive move to someone noticing, and they didn't expect it to blow up.
The reason it blew up is equally simple. Somewhere in the forward chain, someone was close to sunlight, and sent it to them. The original story was going to be "obama promises things about whistleblowers, breaks his promise", but once it got removed from the website, the much juicier story of "obama revises historical promises" came along.
This is how a lot of things in DC get noticed. There are hundreds of staffers and DNC people and what have you. They also likely have a fairly low degree of separation to someone who would notice this, ...