This option is supported on both BSDs and macOS, and ensures the command
also works if GNU coreutils are not installed.
With the BSD (and macOS) md5 command, the -q option is not really "silencing", but it prints out only the checksum in that case:
-q Quiet mode - only the checksum is printed out. Overrides the -r option.
GNU coreutils md5sum does not have an equivalent option: you must always parse the standard output, and take the first printed field as the checksum.
Note that GNU md5sum indeed has a --quiet option, but its meaning is rather different: it can only be used in --check mode, and then its effect is that it does not show OK for each correctly verified input file.
Yes, you are missing that I didn't change anything for GNU md5sum, only for the BSD/mac md5 command. :) Normally its output is something like:
% md5 foo MD5 (foo) = d3b07384d113edec49eaa6238ad5ff00
but that makes it more difficult to parse out just the checksum. This is what the -q option is for.