I personally would rather customers just say no thank you, but I can't speak for everyone. If it is easier for you to give out fake info, go ahead. Cashiers usually know not to enter egregiously fake information and can usually take the hint when you give it out. I don't feel like it's inherently rude to give out fake info and I don't know all the legality of it, but I myself prefer a "no thank you." Keep in mind, I have to respond with something like "Okay, just so you know, that's how we send you coupons and special offers. Let us know if you ever change your mind."
The fake info tracking catches the obvious stuff, i.e. 555 prefix phone numbers, names without vowels (yes I know those do actually exist), fake cities, addresses like '123 Random Back Alley', using celebrity names repeatedly, using your own information repeatedly to get credit, just to name a few. A few of those could be attributed to typing errors, so they usually only approach someone if they have many, many flagged entries. Although, last year at least three associates in the district got caught entering false info, so the pressure to meet the goal is definitely there.
In the long run, that's their problem to deal with, not yours as the customer. In all honesty though, on days when most of my customers have been mean about refusing to give information I have been known to find an extra coupon for the first customer that says 'no' politely and with a smile. I goes a long way to make my day better, so I want to pay it back.