The times I've been asked to go to a table it's always been American tourists, I assumed it was only there that it was a 'thing'. I agree that a lot of people think we all want to be TV 'chefs', some of actually like cooking instead of rockstardom.
I've had a table of 4 women asking me to go up and drink with them before, probably the most tempting one but still a no from me
I've also had people wander into the kitchen before, the kitchen door is near to the customers toilets so they see it unfortunately. I actually have a sign on the door warning of bad tempered trolls within, probably makes it more interesting when they're tipsy I suppose. When it happens I just get all Gordon Ramsey like and tell them it's illegal for non-staff members to be in a food prep area. I think, in this country at least, you can generally get away with being a bit surly and anti-social thanks to Marco Pierre White and Gordon Ramsey giving everyone the impression that we're all arseholes, it's kind of what people expect.
Recky, even with the open kitchen, never make eye contact, don't even acknowledge their existence, they may feel less snubbed if you do the whole artist focused on his labour of love. If anyone does try to talk to you give them a slightly confused look and point them towards a waiter