First of all, every kudos for Jon Stewart’s hard work. And I mean a lot of hard work - every successful entertainment host puts in tremendous amounts of effort each and every day. And the results of that hard work is access to the White House.
Congrats to him on that; but ‘secret marching orders’ from Obama? I mean, really... OBAMA? There has never been a more lazy man in the White House. Some of his staff might be giving orders, but Obama couldn’t be bothered to lift his finger, much less formulate any secret plan to GIVE secret orders.
If you’re looking for a ‘free’ bottle of wine at the taxpayer’s expense? A nice vacation to a far off land? Luxury penthouse living? Obama’s your man. Brilliant political strategy? Hahahahahahahhahahaha
When they say "Obama" they mean the staff. If they'd said the "White House" it might be clearer, but I doubt anybody seriously suggested the president worked out a secret strategy for Stewart to carry out.
And, no, it's not obvious or expected that somebody who a lot of people think of as a news anchor (which he isn't, but a lot of people get their news from him) is having frequent, undisclosed meetings at the White House.
It would be worth making noise about this connection, but it's doubtful that Stewart's fans really care or would change their minds about anything if they found out what was going on.