That’s why South Park (Cartman) skewers FG everytime they have the chance. It’s no secret both South Park creators hate Family Guy and that it sucks.
The punchline “it reminds me of the time ....” by the lead characters has been used and abused that SP picked up on it and made it a punchline in itself.
Now South Park is funny. I’m not a regular SP fan but if I run across it searching for something to watch I’ll let it run. Not for children IMO but I don’t have any so...