You are out of luck, @muffin. The QIF standard uses a P line code for Payee or a description for deposits, transfers, etc. So a bank could put quite a wide variety of stuff in there. Unfortunately, the standard was developed to meet the internal needs of QuickBooks, making it less than desirable for general usage in my mind.
You might look into whether your bank offers other formats for exporting statements. They may have been forced to be a little more rigorous for those cases.
It is interesting to note that Intuit stopped supporting QIF in most of its own programs a dozen years ago, even though they invented it.