The Nexus 6P is supposed to have three microphones. I assume the main mic is in the bottom speaker. There is clearly a mic hole on the back just below the camera hump, so that may be what people are blocking. I'm not sure where the third mic is, perhaps in the top speaker.
It is a little odd that block one of the extra noise cancellation mics on the back of a phone would disrupt call quality (at least in a quiet place). This is a common design and you'd think the obvious use case of speakerphone with the phone sitting on a flat surface would be considered.
Perhaps, once one of the noise cancellation mics is blocked, the phone can't tell what's background noise and what's your voice, so it starts attenuating your voice as if it's background noise?
I'm assuming the 6P using Qualcomm's Fluence noise cancellation, which is what most phones with Qualcomm chipsets use these days. Fluence has always been kind of mediocre as far as noice cancellation goes. The Nexus 5 with Fluence tended to cut people's voice off a lot. I was hoping the extra third microphone would improve things, but it's also the algorithm that matters.
There's definitely better noise cancellation out there. The Audience chip (now called EarSmart) is probably the best. It was in the Nexus One, which had amazing noise cancellation (and also in the iPhone 4). But both Apple and Google dropped it. Samsung put it in a lot of the Galaxy S phones, but has dropped it now too. I assume they just don't want to pay for the licensing. Motorola uses four microphone noise cancellation and their own propriety algorithm, which is pretty good--that's what's in the Moto X 2014 and the Nexus 6, don't know about the new Moto X.
Anyway, you could experiment with covering the hole on the back and see if that's what's causing the problem.