I changed the phrasing of that line - +15 isn't too big a hit as you said, but it does affect every Civ. Yes, it's bad. Overall, the only reason to really do it is to get first attack, or they suspect what you're doing before you're ready. If you're going to warmonger heavily, you might not mind. Still I see reason to want to wait before stacking up penalties, like after you have conquered your first and have that land to boost your military and research.
I also reworded the line below that to, "You made a promise to move you troops from their borders, then broke it!" There is a +40 penalty with the Civ you lied to, but it wasn't obvious in that phrasing. You could leave your troops there of course, so long as you don't attack.
I think it'd be 30 turns for the promise. I believe most of the deals you make follow this standard, but I am not 100% sure. I'll try to document the turn when it happens to me next, so that I can clarify it. Thankfully, one of my next articles is going to be Warmongering, so I'm sure to get the opportunity. That is one I saved for last so that it would be as good as possible.
Hope this helps clarify it.
Edit: So, I just did a test as I realized I had a a good opportunity. I made a promise, then waited 50 turns. The notification that I'd kept the promise never came. On declaring war after 53 turns, nothing happened regarding the promise. I suspect you can't attack for 30 turns after making the promise. Is there even supposed to be a notification for this? I know you don't get a 'good' modifier for it, as it's just avoiding a negative, but I know these come up for Settling and land-purchasing promises. Perhaps that's why there's no deal history for it..