Er, it's all to do with residency, not tax residency, and knowing and maintaining a record of all customers' addresses is a basic prerequisite of anti-money laundering legislation, to which estate and letting agents are subject.
And on top of that, I'd suggest that to take it upon oneself to force the deduction at source of a notional tax sum attributable to a debt owing to a customer, without having a lawful basis for so doing, could be seen as tantamount to fraud
So keep laughing. Or perhaps learn a bit about a subject before you do.