The problem may not be with Fireworks but with the GIF format itself, which uses an indexed color system (hence the color palette that appears in the Optimize or Image Preview panels). Many of Photoshop's capabilities seem to be disabled when editing a GIF, though not all of them. Within Photoshop, try changing the image mode to something other than Indexed Color—e.g., Image > Mode > RGB Color.
This should "unlock" the image and let you edit using Photoshop's full feature arsenal.
Glad this helped!
It's interesting: Fireworks makes it much easier to work with GIFs. You just open up the file and start working. Fireworks doesn't have color modes (Grayscale, Indexed Color, RGB, CMYK, Lab) like Photoshop, and is much more geared towards hex codes—which I'm guessing is what indexed color systems use. This makes sense, as it was built to be a web graphics editor.
Apparently, GIFs don't support layers. Fireworks will let you add layers to your GIF, but once it's time to save the file, it'll let you know that you must either save the file in a different format or else the result will be flattened:
Photoshop isn't nearly as friendly to GIFs. Depending on the action you choose, you might get a clue about the need to convert to another color mode, like this one that appears when attempting to use the Dodge Tool:
Just as often, though, you'll only get greyed-out options or an angry "boop" sound from your computer—like when you double click on the locked "Index" layer—with no information provided. I think the engineers could improve this by adding a similar alert message to the Dodge Tool, or even better, by offering a prompt with the option to convert the image to RGB directly (when a user double clicks on the locked layer).