We are having the same problem here in southern Virginia. They stealing the condenser for the copper.
To the customer state your opinion and concern.If they say fix it then do the best job possible and when something else breaks or time to replace it you will be the first they call.
AS as customer...
Do what the customer asks. You did your job, telling the customer his options. If a customer goes against your oppinion, they weighed their oppinion against yours. Your issue should be documentation. Write your recomendations and the real problem on your work order, or whatever you HVAC people call it. CYA.