Yup this is sometimes done, where the third party stuff is served out of a first party subdomain instead of a third party domain. It's still uncommon except in the big publishers because it requires more effort to do the integration.

The topic of "accurate metric" is also challenging. When I worked on this, I would often find discrepancies of up to 5% depending on the technical implementation of the metric. There was never a clear explanation, just that the sequence of events from mouseover to click to redirect to more redirects to the final landing looked more like a very wide funnel with leaky correlation than the straight pipeline you might naively assume.