You're generalizing; just because one recruiter used this as a lame excuse does not equate it to being policy at a company of hundreds (thousands?) of recruiters.
This was from the manager I would have been working for. Like any large organization, there are exceptions and he could be the exception rather than the rule. From my perspective, "Google" cared about degrees.
Is it a lack of a degree or a lack of a relevant degree? Like, if you had a BA in History but were a very competent programmer, would your lack of a STEM degree be held against you as much?
Obviously they were happy with my competency since I was offered a job, they just took the path where they used my lack of degree as a negotiating tactic.
Turns out there are plenty of other places that don't care about degrees and offer more money, so I accepted a job somewhere else. It was an easy decision at the time.