The note you speak of was secured with assets that AA sold for twice plus the note's value
That note had also been refinanced every one of several previous years
It also came with an automatic extension
The cash position you reference was at the absolute lowest, after the deal was made, and TW abandoned the usual winter "cash conservation" strategies and paid that note and other trade creditors due.
As many have noted re the AA BK, it is certainly possible, and common, for companies to manipulate the numbers in order to facilitate their goals. Cash position especially...
We also know that BK does not necessarily, or even normally/frequently result in airlines going out of business.
There was, absent the AA deal, a special BOD meeting scheduled the first week of JAN to hear the final presentation by turn around firm J Alix assoc, a deal/plan that already had widespread support on the board, among the union reps on the board, and with the major creditors, including Boeing, the largest creditor.
There was also reportedly outside financing/investment available for that plan, from the same group that was supporting CAL and AmWest at the time, and a vague outline of a code-share/JBV based "virtual merger".
All of that became moot with the AA deal, of course. The meeting with J Alix etal became the meeting to approve the AA deal that Compton and Carty had worked out.
What would have happened absent the AA deal is, still, truly, purely... speculation.
(Since the next step is referencing testimony before Congress and the DOJ, that testimony was given months later, after TW had accepted and spent DIP financing, culled the most lucrative flying from the schedule, suffered the bookings drop associated from the Asset Purchase Agreement required Ch 11 filing, and acquiesced to AMR's scheduling wishes. Not to mention abandon and actively campaigned against any other deals or restructuring plans.
The testimony was of course true when given, and equally not applicable to a TWA absent the AA deal.)