Saving JPEGs Via an Action

Yeah, I just tested it and it doesn't work. Since you're saving to a different file format, it has to be Save As, not Save, and the path has to be specified.

Actions always have recorded the full local computer path to the file. What is optional is to include or exclude the filename. File > Automate > Batch can override the action save as location, but if using the action outside of Batch then it uses the recorded path to the directory/folder used when recording the action. The other alternative is to insert the menu item into the action, rather than recording the path. If the path is recorded, then the modal control to the left of the action step can be activated to make the save step interactive.

• In the action, include steps to make the file fully compliant with the jpeg specification (8 bit, flattened, no alpha channel*). Then you can use Save instead of Save A Copy.
• When recording the action, make sure the file name and path are not highlighted and not recorded in the action. Just hit Save.
• In PS preferences, make sure "Save to original folder" is checked.

I haven't tested this, but if this doesn't work nothing will. Then you need a script.

*to remove alpha channels, you need to call this very simple script, which can also be recorded as "insert menu item":

activeDocument.channels.removeAll();