SRE (Site Reliability Engineers) according to Tom Limoncelli (a Google's SRE) is a kind of sysadmin, I doubt that this would ever be the case.
I would think the senior SRE engineers know enough about the code base to poke around and make suggestions ("found a bug in module.py at line XYZ that causes bad performance when thousands of users hit it"), but I got the impression that most of their top developers probably would be bored in SRE.
The thing that is ironic is that most of the people interviewing me were not in SRE, but were pure developers. How many companies do you know that let the developers interview sysadmins? I had guys asking me CompSci questions I hadn't heard since college. If the tables were turned, do you think I'd be asking a prospective developer a question about how to configure DRBD replication and heartbeat from one Linux server to another? Even though some devs might know these things from hobby-like experimentation in their free time, they are not going to be doing it on a day to day basis.
It just strikes me as a very broken interviewing system when you have developers interviewing sysadmins.
SWE-SREs have to pass SWE interviews. I work down the hall from Tim. Nobody keeps track of who came in through which side (SA or SWE), but some of the SREs I work with wrote large parts of the services they support.
Sounds like your recruiter messed up.
The software engineering SRE's work on products to make sure they are ready to scale or if something fails to fix the point of failure. They work alongside the product development teams to make sure the product is stable in production.
The two positions require two different skill-sets (I was interviewed for both sides of SRE). One requires very much computer science, data structures, programming languages, and all of those, the other sysadmin requires more knowledge about Linux, its internals, and the command line interface.
(Answer: a lot.)