I’m not sure how I’ve managed to use rsync for so many years without ever noticing this, but hey, you learn something new every day!
[cperl@localhost ~]$ rpm -q --qf '%{name}-%{version}-%{release}\n' rsync
rsync-3.0.6-12.el6
[cperl@localhost ~]$ touch foo
[cperl@localhost ~]$ stat --format "%y" foo
2015-09-24 14:07:05.349357260 -0400
[cperl@localhost ~]$ rsync -a foo bar
[cperl@localhost ~]$ stat --format "%y" bar
2015-09-24 14:07:05.000000000 -0400
[cperl@localhost ~]$ cp -a foo baz
[cperl@localhost ~]$ stat --format "%y" baz
2015-09-24 14:07:05.349357260 -0400