The dog with puppy videos

The show: Family Guy
The episode: "The Man With Two Brians," first aired November 9, 2008, and rerun just this past Sunday.
What happened: After Peter gets a new dog (whom he calls "new Brian"), old Brian tries to regain the affection of the family by playing his puppy video. The video shows him coming out of a basket and doing other cute puppy stuff.
Why it doesn't quite make sense: According to "Road to Rhode Island," Brian was born in a puppy mill in Texas. He was separated from his mother early on. At some point between that time and the first season of Family Guy, Brian wound up homeless on the streets of Quahog. According to "Brian: Portrait of a Dog," Brian was an adult dog when he cleaned Peter's windshield and Peter decided to adopt him.
Now, this doesn't rule out that someone would have shot puppy videos of Brian. But how exactly would Brian manage to hold on to that footage throughout his tortuous path from Texas to Rhode Island? When he was homeless, would it have been a priority for him to protect a video tape? The only explanation is that the writers have forgotten the character's backstory and thus created a continuity breach.
In a comedy, a continuity breach is forgiven if it yields a very funny joke. The bigger the breach, the funnier the joke has to be. But this continuity breach is used exclusively for the purpose of creating schmaltz, and not for a joke. With Brian's puppy videos, Family Guy has jumped the shark.