I like the tac solution; it's tight and elegant, but as Micah pointed out, tac is part of GNU Coreutils, which means that it's not available by default in FreeBSD, OSX, Solaris, etc.
This can be done in pure bash, no external tools required.
#!/usr/bin/env bash
unset comma
read foo < parse.txt
bar=(${foo//,/ })
for (( count="${#bar[@]}"; --count >= 0; )); do
printf "%s%s" "$comma" "${bar[$count]}"
comma=","
done
This obviously only handles one line, per your sample input. You can wrap it in something if you need to handle multiple lines of input.
The logic here is that we can convert the input into an array by replacing commas with spaces. Of course, if our input data included spaces, this would have to be adjusted. Once we have the array, we simply step backwards through it, printing each record.
Note that this does not include a terminating newline. If you want one, you can add it with:
printf '\n'
as a final line.