I think on most falls people get away with it. I had a crazy number of falls early on trying to "play catchup" late into the game .. first broken ribs were on a very large fallen tree - you'd almost call this a flat injury rather than an object - if the speed and angle are just right .. splat....
As
@flash says, you can generally get riding again if you want. It's just vitally important that you armour up as you don't want to injure yourself if you already have a fracture, it can cause all sorts of far worse problems. If you're patent, it can be better to just wait. I'm not. I also find if I wait I have all sort of other problems from not doing things. I also find getting back on the bike puts me in a better place psychologically when healing.
For Front ribs I find I can ride in a few days, but you have to be really relaxed and can't get too physical, if you tense up it will hurt like hell. Depending on the fracture, pain levels can start diminishing after a couple of weeks. My latest ones are easing off at 4 weeks, but it's generally 6 weeks before you don't give them a second thought and they're normally fully healed.
For back ribs, I find I can't ride until they're further on the road to healed. They just hurt too much for me. The last ones I think it was about 3 or 4 weeks before I felt I could hold myself on the bike properly (that was a horse kick though, so was a fairly brutal impact that knocked me 6 meters through the air).
I find after each accident I end up re-evaulating my protection. Ultimately you can't armour for every eventuality and you have to find a balance with heat and movement. You still need to be comfortable and able to ride.
Hope you heal up quickly. Icing 3 or 4 times a day should speed things up by reducing inflammation. Arnica also seems to help with breaks.
Ultimately, I think most will be from an object, but if you carry enough speed or just land at an unfortunately angle, there can still be a huge amount of energy being applied. My latest were from a double tree stump hit with substantial force to the chest. I was lightly armoured. Light armour will stop/reduce a huge number of injuries won't stop a break with a focused impact though. If I'd not been lightly armoured I really wouldn't like to think what kind of physical damage I would have. As it was I bounced off the stump, hit a tree and some logs then ricocheted off down trail. It really really hurt .. I passed out ..