Run SQL Server 2016 side-by-side with older versions?
At the risk of speaking directly for @BrentOzar - I don't think he's saying you can't install SQL Server 2016 alongside a prior version.  His blog post1 states:

You probably shouldn’t run 2016 side-by-side with older versions because:
... You may get updates whether you want them or not.

This does not say you will get updates that will bork your box.  Essentially, any Enterprise installation of SQL Server should be carefully managed - you probably shouldn't allow automatic updates of SQL Server at all, and I'd be quite afraid of letting Windows Update install any updates automatically without some kind of pro-active management.
Test your planned deployment on a non-production box to see if the installation of SQL Server 2016 will cause problems for your environment.  Then make an informed decision about how to go about applying updates.  Decide for yourself if you can afford the risk of a side-by-side installation, versus the extra cost of running multiple SQL Server boxes.