It turns out you can't use CopyResource in feature level 9.x when the source texture has a shader binding flag:
And I guess the driver was not handling it well. On the up side, I did get it working by copying into a rendertarget texture without a shader binding (which does limit the formats some), and then saved that with no issues.
Feature Level Behavior Differences
D3D_FEATURE_LEVEL_9_1, D3D_FEATURE_LEVEL_9_2, D3D_FEATURE_LEVEL_9_3:
Only Texture2D and buffers may be copied within GPU-accessible memory.
Texture3D cannot be copied from GPU-accessible memory to CPU-accessible memory.
Any resource that has only D3D10_BIND_SHADER_RESOURCE cannot be copied from GPU-accessible memory to CPU-accessible memory.
As for the first part of the issue, well, I guess the D3DX functions aren't very friendly when it comes to saying it can't save a file format with specific texture formats. My solution there was to just copy to a temporary R8G8B8A8_UNORM texture and save that instead.
Now, I do have one last question:
The solution for the feature level 9.x issue is not ideal. Mostly because some formats can't be used as a render target. So, I wondered if I could use CopyResource to copy it to an ID3D11Buffer? And if this is indeed possible and since the buffer requires a size in bytes, how would I go about calculating the size of a texture in bytes (uncompressed)? I could go through each mip level, get the width/height and multiply by the pitch and add each mip size together. But if there's an easier way, I'd like to know what it is?