In my experience the VAST majority of customers will readily accept that a stain of that type and age will not come out and so it is far better to seek their agreement to that than risk a very risky procedure that if it goes wrong and you make the stain worse, you own the carpet.
For all we know they could be getting it cleaned as a last ditch effort before having to replace it. If you make it worse, suddenly they have someone to blame and and boy will you hear about it.
It is far safer to explain that you can sanitise it and give it a thorough clean which MAY improve it, but you can't guarantee it. If they won't accept that and insist on complete removal - walk, it ain't worth the risk of the 'rocket science' approach, espcially when there is a common sense approach that carries no risk.
Simon