You need to have a file manager of some sort that will allow you to navigate your file system to select an arbitrary file. If you do, when you select either attach picture or attach video you will get to select the file manager and pick any file. If you don't have a file manager, install one like ASTRO File Manager.
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As I said at the top of the thread, you can install a file manager like Astro File Manager. That will add itself to the save as menu and allow you to select a file location.
I don't know why you're insisting on repeating wrong information. Native Android behaves just like these posters say it behaves. YOU have installed at least one third-party app. Do you think Dropbox support is native? Or maybe you installed a Dropbox app, which is functioning as a file manager? I wonder.
You're not listening. The poster states that his Attach, Picture actions are limited to Gallery and Dropbox. That indicates he doesn't have a file manager to handle the operation. If he installs one, it will show up as an additional action on that menu. It's really simple. Each file manager that he installs will be a way to navigate the file system and select an arbitrary file. What would Gallery defaults have to do with it?
Because that's the way they work. When I do Attach, Picture I see, in addition to Gallery, all of the several file managers I've installed, by name and logo. Once they register themselves with Android as file managers, all pertinent contexts for file managers automatically list them. That's why installing the Dropbox app automatically makes it available as an Attach, Picture option. Regardless of why they don't have a file manager installed, the easiest way to fix it is to install one. Or more. I have four or five. There's no downside to having options.
My phone didn't have a native file manager out of the box. It sounds a lot like a couple of other users' phones didn't have a native file manager. There are a lot of references to Android not having a native file manager, like:
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