You’re mainly right. If you vouch for a person, then you’re letting people know you trust that person and can attest to their actions. It doesn’t necessarily mean you agree to take responsibility for the actions of that person.
If you vouch for someone, you also put your reputation on the line as that person would not ordinarily be taken serious without your word. And if the person takes a loan with the help of your influence and doesn’t pay back, you won’t be held liable to repay the loan. Unless of course you agreed to pay if the debtor doesn’t pay.
You could also offer to willingly pay back the loan in order to protect your reputation cause when next you’re vouching for someone, People may not be that willing to accept just your word.