It does allow that and also workers or peers in other depts.

“If I was mowing lawns would it be appropriate for me to write a PEER Praise Note to the Director of Public Works or the GM?”

If you were just mowing lawns you wouldn’t get a peer praise, possibly a verbal thank you as it’s probably your job. However if you’re mowing lawns and do something not your job that goes above and beyond the normal scope of your job (and I don’t know what that might be off the top of my head mowing grass) then if a homeowner saw it they may call PW and tell Eddie who might choose to write it up, giving a copy to the you, one to the GM and one for your file. If a peer saw it, they may ask to have one written up on their co worker, they may not. The person doing the action is the one who gets it, not the supervisor of that person.