They could send my wife and I to jail for not paying the debt?

The part about the agency not having to negotiate is true; it’s purely voluntary whether a creditor or debt collector will enter into debt collection negotiations with a debtor, or whether they will hold out for payment in full.

However, the part about the agency being able to throw your wife or yourself in jail for not paying is not true. People are not jailed for consumer, medical, real estate, etc. debt incurred in good faith, simply because they cannot pay. (If someone commits fraud—deliberately steals money by deception—in the process of incurring debt, that’s a different story.)

Moreover, a debt collector or collections agency may not threaten a debtor with prison. That’s barred under federal law, as well as under the law of many states. The collections agency is itself breaking the law by making this threat, and you could report them to the appropriate government agency.