What is being given up is data, but this isn't referring to the limiters your team will give to Twitter ("we want 18-24 year old women who have Tweeted about clothing in the prior 96 hours and who are nearing our store between 9 AM and 10 PM"). The data at risk are the responses.
Let's say you broadcast these discount messages to 4,000 proximity shoppers and 300 react, 250 download the coupon and 86 redeem the coupon. You won't be the only one saving those 86 names in the "nice" list, the one that you'll want to check a lot more than twice. So will Twitter.
And Twitter is likely to share those enhanced names with others, albeit at a much higher price. They are your customer and you paid for that contact. And yet it will be Twitter who be selling it at that higher price—and quite likely to a direct rival who would kill for shoppers who are confirmed to like your store.
It gets worse. Now your rival knows what this shopper redeemed and when, but also the time she replied to that Tweet. You’ve wrapped up your customer very nicely for your rival.
Alternatively, you could do your own geolocation campaigns using your app—and keep all of that data where it belongs. Working with Twitter and Facebook and Google are going to be the hot tickets this holiday season and they'll gladly do all of the heavy lifting for you. And, yes, that will be a mischievous twinkle in their eye.