I'd have nothing against it, if it wasn't such a legal tangle. Seems easier to send them on - but then, I do have an abbotoir about 10 minutes up the road (sheep and cattle only). I take my neighbours pigs on too and the nearest place that does them is 40 miles each way, much easier to take em somewhere quiet and do em on the farm IMO, but looks like the legislation is moving further in the other direction.
However, the point is that plums doesn't want it done on her place and its a fairly odd assumption to make by her tennants that she's okay with it. If I was her I'd just say no outright and not try to justify it.
(having said that - I've had to shoot a lamb who was beyond salvation on my grazing once, and Id be very surprised to be asked not to do it, but I think the situation in that case is slightly different).