Basically as long as you rename the 'save-as' file the exact same name as previously, you should be fine. The issue is that you should not have to rename when using 'save-as'.
If you do not re-name the game automatically renames it for you along the lines of 'savegame 3' (or how many saves you have up to that point). This is causing players to become confused as to which file is what.
The next issue is then when using 'save' the game automatically saves the currently being played game as the last game played. This makes it super easy for save games to get rewritten basically, if you started playing a different game. (Or in other words, if the game you are playing now is a different save file to the one you played last.)