Interestingly, the other two couldn't remember the rule, either. If only they had taken the time to march downtown to the Grammar Law Library and look it up in the Grammar Penal Code, they could have cited number and verse the rule I had violated and even told me the penalty for my grammar crime.
I'm being facetious, obviously. But the point is that, in grammar, there are no official prohibitions. Does that mean that language is a free-for-all? That anything and everything you might say is fine?
On the contrary. A sentence like "Cake us me serve will" is undeniably wrong (except, maybe, at Yoda's house). But that's not because there's a rule against it. It's because that sentence does not conform with the mechanical process we call grammar.
For a usage to be "wrong," it must be either 1. ungrammatical, or 2. contrary to dictionary definition ("This wine compliments this meal" instead of "complements"), or 3. unidiomatic — that is, inconsistent with generally accepted constructions ("I dissociate myself to this matter" as opposed to "dissociate myself from").
Which brings us back to the original question: Was I wrong to write "him seeing" instead of "his seeing"? The answer is subtle and it has to do with our first criterion: grammar.
Verbs like "risk" take direct objects, which are nouns (Dave risked his paycheck) or pronouns (Dave risked it). Gerunds, which are "ing" words derived from verbs, also qualify as nouns and can be objects of verbs (Dave risked dying). Objects of prepositions like "of" work the same way ("the risk of ruin," "the risk of it," "the risk of dying").