I was a regular support drone as far as anyone knew.

I just had some connections that came about because I could be discrete and the engineers understood that I didn't bring them garbage too early (without enough information) or without good reason.

Parent likely established a working relationship with individual(s) in engineering organically over time, and at some point leveraged that relationship to ping them about a customer issue that crossed their path and seemed to be an engineering concern vs user-error. That didn't cause waves and went well, and got repeated enough to become an established but unofficial "thing" parent was capable of, and they became known by a few sales/account folks as the go-to person when they felt a situation may warrant that unofficial route.

You can make a career off of doing this sort of thing, but I'd caution against it. If a company is hiring for specific scenario of "fast lane between client and engineering", the actual job is "support with special escalation privileges, servicing clients splurged for the premium package". You get all the soul-crushing hell of working a normal support role, but with the added benefit of solely servicing clients that expect you to hand them the world because they paid extra for it. Which is far closer to a nightmare than a dream; particularly considering someone working one of these official roles likely has the skills to pivot out of the support org and into the engineering org in some capacity, and drastically increase their salary potential while simultaneously improving their quality of (work) life.

In a more general sense though, pretty much any career benefits from doing what the parent described. It's effectively just flexing your soft skills and establishing relationships with people outside of your immediate sphere/department. Which has a tendency to make it easier for you to get things done, and garnering a reputation to that effect.

But above all: be a good listener. Listen to what they say, think about it and build it on next time you talk with them. If they see you showing interest and learning about their domain, you'll get a direct line to them. And don't always bring them problems, be sure to stroke their ego too by asking what they're working on.

It doesn't happen overnight, it requires perserverence and a dollop of luck. You won't walk into a job like that, it takes years of building a reputation for yourself.