First, the pig comes swaggering past an open door:
Next, Mrs. Bennet stops beside another open door at the top of some steps and calls through a little room, toward where the pig was:
Last, Mr. Bennet follows the pig into view outside that first open door and engages Mrs. Bennet in a little conversation:
Now, examine these pictures. What's that beneath the pig's feet? Looks like sawdust or chaff to me. Not floorboards or even flagstones, certainly. When you look at Mr. Bennet, you can see all kinds of things wrapped in fabric and hanging from hooks -- those look an awful lot like cured meat to me, at least compared to what I've seen at all the living history places I've visited over the years. That is clearly some kind of cellar or place for storage, possibly even open to the elements a bit -- you can see sunshine pouring in from behind the pig. The flooring in that dividing room is dirty slabs of stone, probably some sort of entry way where the servants bring things in, store things for the kitchen, whatever. The chair we can see in the first picture certainly doesn't belong in any of the nice interior rooms where the family lives. The walls in the middle room aren't painted either.
But look at where Mrs. Bennet is -- that's the part of the house where the family lives. There we see painted walls and some sort of light fixture. It looks to be the hallway leading to the front door, as several of the girls race past her in a few more frames, all ready to go to town to see the militia.
So. Do the Bennets have a pig in their house? No! They have a pig being herded by Mr. Bennet and an employee through a storage area (underneath the remains of some of its previous companions, no doubt -- the pig's, I mean, not the employee's). The only animals ever seen in the house itself are a couple of dogs. Fitting household companions for a gentleman.
Ladies and gentlemen, to me it is clear: no pig in the house.