I was baffled enough by this comment to take my copy and look. The Nullstellensatz is an exercise late in the book long after Noetherian rings are introduced and they don't even do the Rabinowitz trick in the hints as they have enough theory to hit it the hard way. Determinants are nowhere to be found.
The ability to decrypt depends on figuring out that the sharing scheme has your pieces covered, and knowing that you have in fact covered the right thing because of a bug like this is hard to do. There are some ways to test the sharing scheme that might have caught this, and looking at example shares carefully should have, but it's a bit more subtle to make generic tests.
Search frictions are real lots of bad candidates clog up the market and your assessment process/ other things might not be getting who you need in the door.
Social media and dating apps together have created this isolation. People can demand a completely comfortable illusion of life and enforce this sterility.