A coupon code should not go through on your store unless you have created/authorized it in your discounts module in the admin.
We haven't had any issues with Honey. However, we have had issues with a certain coupon aggregate site (which we hadn't previously heard of) advertising that we are offering discounts/specials/sales that we have never offered before, and handing out coupon codes that don't work on our site, which has led to some customers complaining that we are advertising and then not honoring these specials/coupon codes. We have put out a notice on social media and via newsletter that we have not advertised with this coupon site, nor have we authorized the specials & coupons that they are advertising on our behalf. If the issue continues, we are considering issuing a cease and desist letter to them.