I think it may be worthwhile pointing out the practicalities here - i.e. "I can try to cover up, but it will probably mean that bub will be much louder and more people will notice than if I just fed him in the usual way". And then put it back on her - i.e. "You want private feeding then find me somewhere private with a comfy chair". At least that way you will probably not wind up having to feed on uncomfy reception centre dinner-eating chairs.

At wedding receptions I took bub away to the foyer - not at all private, but people were just passing through rather than having to see boobs with their dinner (cause we hadn't a hope in hell of using a wrap). And of course that was where the comfy couches actually were. In a church I would probably also have used the foyer.