rustup install 1.16.0
should definitely work, I use it all the time for testing against various older releases. It will not touch what rustup considers as the stable toolchain, as far as I know there's no way to downgrade that.
In terms of help messages, rustup help install says
'toolchain' specifies a toolchain name, such as 'stable', 'nightly',
or '1.8.0'. For more information see `rustup help toolchain`.
rustup help toolchains then also says
Standard release channel toolchain names have the following form:
<channel>[-<date>][-<host>]
<channel> = stable|beta|nightly|<version>
<date> = YYYY-MM-DD
<host> = <target-triple>
'channel' is either a named release channel or an explicit version
number, such as '1.8.0'. Channel names can be optionally appended with
an archive date, as in 'nightly-2014-12-18', in which case the
toolchain is downloaded from the archive for that date.
Obviously @vchekan missed the "or an explicit version number" part somehow, I'm not sure if there's a simple change to the text that would make that stand out more.
Technically rustup install stable-YYYY-MM-DD does work as well, with a bit of digging into the manifests I found rustup install stable-2017-03-11 works for installing rustc 1.16.0 (30cf806ef 2017-03-10), although I see no reason to use that instead of rustup install 1.16.0. Again this doesn't touch what rustup considers to be stable, it just gives you another stable-2017-03-11 toolchain you can override to.