'Personally for me, his not saying anything at all was just too much.
That's the safest form, in my opinion. 'Saying' has some verb-like characteristics - it has 'anything' as its direct object - but it is also functioning as a noun, the subject of the verb 'was'. As 'he' cannot be the grammatical subject of the non-finite 'saying', the possessive determiner is the logical choice for the noun 'saying'.
Having said that, I think you'll hear all three, he/him/his, being used.
Last edited by 5jj; 13-Feb-2012 at 20:24.