Assuming the fine is one-off and market doesn’t devalue facebook because of the fine itself, couldn’t Facebook issue new stock to offset the fine, effectively losing 3% of stock value in the end?
Look at it from the perspective of existing investors: They would be forced to buy the new shares Fb is issuing in order to maintain their respective percentage of shares and, thus, their expected future dividends. There's nothing to gain from that – in fact, their investment's expectation value just goes down as they now need to pay an additional price for the same expected future return. Needless to say, shareholders don't value such a move, so any CEO trying to pull off such a thing would likely be removed immediately.
What about not getting shut down for failing to pay a fine?
But even in these situations, I think a case can be made for why refinancing the company by having it take a loan is still more attractive. While from the perspective of an existing shareholder it will reduce future dividends in a similar way as new stock, there will at least be no opportunity costs. (If the company issues new stock, the investor has to consider what else they could do with their money instead of throwing fresh money at the company.)