I'm not sure what you mean by "hard evidence," but it seems that you're misrepresenting Partington's position. In the preface of his book (dating to May 1959), Partington writes:

If the dates of the texts are correct, the discovery of the use of saltpetre in explosives and the development of gunpowder are to be sought in China from the eleventh century.

So Partington does believe that the most likely origin for gunpowder is from China. Even the blurb on the back of the book makes this clear:

His book includes chapters on gunpowder and weapons in Muslim lands, India, and China- including fire books, the use of gunpowder as a propellant, the artillery of the Mughal emperors, and the use of saltpeter in explosives. He traces the development of gunpowder to eleventh-century China and cites the first known mention and picture of a firearm in 1326.

Additionally, Partington's book was written 55 years ago. A lot of research into the history of gunpowder has happened since then, most notably the publication of Science and Civilisation in China: Military Technology: The Gunpowder Epic in 1987. These are Bert Hall's concluding remarks for his introduction to the 1999 edition of A History of Greek Fire and Gunpowder:

There are works which, however flawed, represent milestones in the development of scholarship and occupy an important niche. Partington carved out for himself an indispensable place in the scheme of things. He is the trustworthy guide, the Moses who led scholars out of the wilderness without actually entering the Promised Land. Partington's Cambridge confrere, Joseph Needham, whose monumental Science and Civilisation in China contains the definitive history of oriental gunpowder, depends on the chemist's earlier work at every turn, while adding Chinese evidence that was unavailable when Partington was writing. Needham complements Partington, making the kind of broad, sweeping, interpretive generalizations that Partington avoided. Needham and Partington together have laid the groundwork for all further effort in the early history of incendiaries, explosives, and propellants. Everyone who researches and writes on this subject will be forever in their debt.