Setting aside your partial jest, I think Google's approach of hiring "programmers" to fill the role of SRE makes perfect sense for their organization.
The "sysadmin" can have a wide range of meanings and responsibilities but many will have experience managing COTS[1] software like Oracle RDBMS, Peoplesoft HR, MS Exchange email server, etc. A typical system admin can then use complimentary COTS tools like Microsoft SCOM System Center Operations Manager, HP OpenView, IBM Tivoli, CA Unicenter/Spectrum. On Linux, it would be similar tools like Nagios, Zabbix to monitor Apache webservers, Mysql, etc.
In Google's case, they didn't cluster a bunch of COTS Oracle dbs together to serve web surfers. Instead, Google wrote a proprietary platform like BigTable or Spanner[2]. As a result, they also want additional software that monitors the health of Spanner. Since none of the monitoring tools from enterprise vendors like HP/MS/CA are adequate (because they have no out-of-box software-agents for Spanner), they need another layer of programmers to write custom management/monitoring tools. Those programmers are the SREs.
All the above enterprise tools from HP/MS/CA/etc including the mother db server, the agents, the plugins are written in C/C++. If your hiring job description is "system admin", most candidates will not have the skills to develop those enterprise monitoring tools from scratch. Yes, many sysadmins have programming skills to write Bash/Powershell scripts. E.g. a bash script might have a polling loop that checks for an error file existence and then has if/else/fi to send an email. However, that's not the same programming skill as developing a proprietary version of HP OpenView and MS SCOM. Most traditional sys admins do not write low-level C code like Zabbix.[3]
Basically, if you're a company that writes complex proprietary softare and none of the existing enterprise monitoring tools can manage it, you'll have to hire programmers instead of sysadmins as the baseline skillset for SREs.
[1] https://en.wikipedia.org/wiki/Commercial_off-the-shelf
[2] https://en.wikipedia.org/wiki/Spanner_(database)
[3] e.g. https://github.com/zabbix/zabbix/blob/trunk/src/zabbix_serve...