No, that is not the case. Apple certainly did not "need" an infusion of cash from Microsoft. That is the rumor that Microsoft started spreading several years after the event perhaps to save face.
Apple had almost 1.5 billion dollars in cash in the bank when Microsoft bought $150,000,000 in preferred stock as part of a lawsuit settlement that essentially Apple won. MS was required to license certain software patents from Apple for a minimum five years, purchase the preferred stock in lieu of a cash payment, and continue producing and developing MS Office for Mac for another 5 years for undisclosed yearly payments while Apple was allowed to license a few software patents from MS in perpetuity at no cost.
For Apple's part of the settlement agreement, they agreed to make Internet Explorer the default browser on their computers (but they could continue bundling Netscape Communicator in every new Mac as well), issue some paper in exchange for the $150,000,000 (which cost them nothing), and bundle trial versions of MS Office for Mac with every new Mac for a period of five years.
Microsoft sold the preferred stock on the open market about three years later for a substantial profit. They retain none of it today.
Nobody trades preferred stock for money after winning a suit, you just take the money. And there was no rumor spending after the fact it was KNOWN at the time that Apple was losing money hand over fist, their stock was in the toilet, their market share was down, and then in came MS with an infusion of cash but most importantly an agreement to keep making product for Mac. The face saving here is from you saying this was the result of a suit. Why would MS need to save face, as you point out they sold the stock at substantial profit, they rode in for the rescue and made a boat load of money on the deal, nothing there that requires face saving.
Apple was in trouble during those years, they probably didn’t really need the cash that bad, while they were losing money they’d developed a serious war chest, but MS was threatening to pull out of making a version of Office for the Mac, there wasn’t very much productivity software for Macs at the time and if MS had pulled out there would have basically been none. That could have killed them, it’s hard to sell computers with no productivity software available. Thanks to the preferred stock MS kept making Office for Mac, and kept it a viable platform for doing stuff other than special effects.