Adding a new PC to the party means inviting an unknown and dangerous-looking stranger to join your group of otherwise paranoid and greedy adventurers. There's pretty much no way to roleplay it so that it doesn't sound stupid.
Imagine if someone did this to you in real life: You're walking down the street and bump into a three random guys who invite you to to join in on assault and robbery; offering you a one-quarter stake in everything and a very real chance at severe bodily harm, without bothering to ask for your name or qualifications.
It's ridiculous. That sort of thing never happens unless you're in Detroit.