Fowler called the construction with an object rather than a possessive followed by the -ing form a fused participle. Generally it's better to use the possessive form of the pronoun but sometimes there is a difference in meaning between the two. Consider the sentence I like Alan/Alan's cooking in my kitchen. With "Alan", I think the liking is aimed at an oft-repeated activity, while with "Alan's" I think the speaker is talking about a specific occasion or series of occasions.

Some words resist the possessive in this context. Her meaning being clear did not make much difference. rather than Her meaning's being clear did not make much difference.

Bingley

Bingley