That phrase came from the fact that the Upload Wizard and the GWT were the only things listed in the "integrated" section of the page [[Commons:Upload Tools]]. However, I see that as of a couple of weeks ago someone's added a new item there too: https://commons.wikimedia.org/w/index.php?title=Commons:Upload_tools&dif...
I'll take your recommendation for how to better phrase this sentence to be both factually accurate, but also to try to emphasise that this tool is trying its best to be "of the system" rather than sitting outside of it.
Hmm, I guess that list is considering user scripts as integrated, which is arguable, but different from my definition (And I think different from what you were trying to get at).
I imagine commons doesn't include the mobile upload feature, as by and large they seem to hate it ;). Perhaps special:Upload isn't included because its seen less as an upload tool, and more as the base system.
Anyways, for the grant proposal, I would maybe use language like:
"It is the only “integrated upload tool” for Wikimedia commons allowing multiple files to be uploaded at once (aside from the WMF-developed Upload Wizard)"
as that makes it technically true, and also emphasizes the multiple file nature which is pretty key to gwtoolset.
--bawolff