I had a job like that. I was supposed to use my analysis and creativity to build models for client forecasting, but if they didn't confirm what the brand team wanted to hear, they'd be rejected. It sucked. I was fresh out of school and cared more about getting the right answer than appeasing clients.

I lasted 8 months in that job. No regrets about leaving.

Also, $16k is piss-poor for a severance package in a brand-name consulting firm like BCG. Given the economy and the likelihood of a necessary career change, OP should have asked for 6 months' base (including COBRA) and an "office firing" (you're terminated but can use office resources for the job search and retain the right to represent yourself as employed).