Would that mean to you for the whole day, staying for lunch, etc. Or would you take it to mean you could just pop in for some of it and make other plans for the rest of the day?
This is the situation with my best friend who was invited "for Christmas Day", so planned and catered for, but she's just said "Oh don't worry about feeding me" (she's a vegetarian) But DP has already got in veggie options. Presumably she isn't going to sit and watch us eat so I can only assume that she's made other plans for the afternoon. If she's done this I'll be really annoyed and upset :( I was looking forward to spending some Christmas time with her.
FWIW she's our only visitor invited "for Christmas Day"