I observed a (non-engineering) team successfully use this argument to avoid being measured at all except through the customer feedback that they were a primary

I observed a (non-engineering) team successfully use this argument to avoid being measured at all except through the customer feedback that they were a primary channel for. As such, they were oft quoted as being amazing. I can't say that they weren't - my interactions with them were tangential to their main purpose - but the work that my team had that depended on them or their input was often not done or missed the point completely (and criticism dismissed as they are the posterchild team). I think you should use surrogate metrics. You should just know them for what they are, and be able to argue as to why they aren't representative when they are bad and when they are good. This means you can't make somebodies job, bonus, or promotion depend on the metric. But it means you do get a heads up when something might be going wrong. And it means you get a heads up when something might be going right. It also means you have to deeply understand what a metric really is, and what each particular metric is to the mission of your company and your job. This is hard.