Those under specified requirements and unrealistic deadlines are both the outcome of poor communications. An adept communicator is able to identify and convey the critical importance of correctly defined requirements. Likewise, such a communicator addresses unrealistic deadlines and explains the reality to those that need such explainers why their unreality is impossible, and they thank the good communicator for their honest language rather than any form of negative reaction. Such is the power of quality communications. An unrealized super power that actually exists in our social civilization.
Furthermore, even if that were true, companies (especially ones like Google) look for project and product managers that have CS degrees or other STEM degrees.
Personally, my frustration with project/product managers often comes from (ironically) underspecified requirements and highly unrealistic deadlines. Neither of those I consider a failing of their education or skills, but a failing of the company's reward structures.