Is Tiny Tim Really Fred's (Scrooge's Nephew) Son

My Wife and I have been watching A Christmas Carol with Patrick Steward for years. Each year my wife picks up on a scene that is really out of place in the movie, & our only conclusion after watching the scene time after time is that Tiny Tim is really not Bob Cratchits's son. In the scene, they are sitting around the fireplace & Bob says that it was strange that he ran into Scrooges Nephew today. He says that his nephew gave him his card & says that he has a good wife & that if Tim needs anything to let him know. Crachit was a bit puzzled as to how Fred even knew of his wife & Tim. Earlier, Cratchit asks his wife "Where did you get such a fine goose (since he knew that he did not have the funds to buy it himself). The presumption here would be that Fred bought the Goose & gave it to Crachit's wife. Normally, I would not mention this on literary forum, but the Patrick Stewart version of a Christmas Carol is as good as it gets, & I want to pose this question to some sharp analytical minds. If you have not seen it, have a look & let me know what you think. Now that I watch this movie, this scene is a blaring reference to something going on with Crachit’s wife & Fred.

There was a slightly odd bit in the book in which Bob Cratchit reports having met Scrooge's nephew, who asks him how his good lady wife was. It was odd because Bob wonders out loud how he knew she was good. I thought it was just an expression. I doubt very much Bob's wife was carrying on with Scrooge's nephew. I can't remember Bob asking about the goose, the notes in my copy of the book said that Bob Cratchit would probably have been in a goose club, to whom he would pay a fraction of his wages for weeks or months beforehand. Personally, I wondered why Scrooge, after seeing them enjoy their Xmas goose, bought them a big turkey. Couldn't he have bought them something else? I was a little surprised the turkey shop was opened on Christmas, and I was surprised the big turkey was still there. I'd have thought the shop-keeper would have discounted it.