Cuba's lawyer, Mark Heller, tells TMZ ... the actor says when his accuser approached him at the NYC club, sitting down on the couch next to him and his girlfriend ... she said she was a fan of his movies, especially "Snow Dogs." If you've seen it, you know why that would stand out to Gooding.

That initial interaction is what you see in the surveillance video TMZ obtained.

We're told, Gooding initially thought she was messing with him because she shouted out "Snow Dogs" over his Oscar-caliber classics, but he decided to be friendly since she was a fan.

As for the touching that's evident in the video ... Heller says Gooding admits placing his hand on her thigh as a cordial gesture -- as friends might do when sitting closely. Then he says he brought his hand up to her hand -- NOT her breast -- and brought her hand to his lips for a kiss. Again, Gooding says it was all a "friendly gesture."

The actor insists he did not touch the woman's breast and wasn't hitting on her ... as he was ever mindful his girlfriend, Claudine De Niro, was sitting in between them.

After the encounter, Cuba and Claudine went downstairs at the club to make out on a couch when the accuser confronted Gooding's security about the alleged groping. We're told Gooding says he had no idea what she was talking about and was confused about who she even was, because he'd met so many people that night. He then got up to leave.

When the case hit the media, Gooding claims he only remembered his interaction with the woman ... mostly because the surveillance video triggered his memory about her love of "Snow Dogs."

As for initial reports about club security having to break up a heated argument between Cuba and the accuser ... Heller says it didn't happen. He adds there are no witnesses nor video to support it either.