Why can't the government do the same with the banks that it did with SiriusXM radio?

SiriusXM was in danger of going bankrupt last week. Liberty Media, aka DirectTV, came in and loaned them $530 million in exchange for 40% of the company. The government did nothing.

Like Ive mentioned before, if we are 11 trillion in debt, that means there is $11 trillion in money around. Liberty Media is worth approx $41 Billion, so they took some of that money, and invested it in a company it thought has some sort of potential or desirable assets.

My question is, if a company like Citi is in trouble, and it is or can be a profitable business, why does the government,which borrows money, have to take a stake in the company, rather than a private firm, who already has money available to invest in other businesses?