That is a bit of a mis-statement. Apple was in trouble at that time, but it was not on the brink of a bankruptcy (despite the constant use of the word "beleaguered' by the press), and Microsoft's investment did not materially affect Apple's ability to continue. The investment was intended as a show of faith from Microsoft (and turned out to be a good investment).

The far more important part of that announcement was the commitment of Microsoft to continue development of Microsoft Office for the Mac. That was the single biggest symbol that Apple was going to continue. Without Office the Mac was likely doomed to an ever smaller nitch, and everyone knew it. That one commitment on Microsoft's part cemented the Macintosh's place as a big player, and kept Apple from dwindling to the point where bankruptcy would have been a real worry.