"near death" is a exaggeration imo.
I don't believe that's accurate. Helio Gracie had a match with Masahiko Kimura, and I believe this is what you are referring to. The match ended after Gracie's side threw in the towel during the second round (The total match time was over 13 minutes). It should be noted that Kimura was significantly younger and larger than Gracie at the time of the match. Also Helio himself did not submit, despite having his arm broken during the match.
There were rounds, although I do not know the length of the round (I would presume 10 minutes). I don't believe the match was stopped for any reason inbetween rounds. Also Kimura had publically stated that if Gracie lasted longer than 3 minutes Gracie should consider himself the winner.
Not to mention Kimura was a judo and karate guy, not a jiujitsu guy, and he had fought man wrestling matches and challenge fights similar to todays MMA. He was probably the greatest fighter alive at that time. No one before Kimura, no one after. If I remember right Kimura refers to Helio Gracie as a little meek 6th dan in judo. He was frustrated that he kept throwing Helio, but the mats were too soft and Helio was unharmed. So he finally pinned him and broke his arm with a bent armlock we now call the Kimura. The towl was thrown in and Kimura was the winner. This was a grappling only match. However bjj has come a long way from the gracies. With each new black belt comes a revolution of techniques and new ideas and refinement of old ideas. Things that were once lost are rediscovered and new things are lost. It evolves and is not a fixed art. I'm truely amazed everytime I watch a new blackblet. Guys like Eddie Bravo, Braulio Estima, and the late Carlson Gracie all have very unique ways of using bjj. So its not as simply as beating bjj with an aikido technique ( as if there was a technique you could use to defeat anything 100% of the time). Its a matter of defeating the unique style of the fighter you face.
This is why there are guys who are better then I that I can tap without issue, they simply can not deal with my style. Likewise there are guys who technically I am better than, but for the life of me I find a huge challenge. Guys I can tap without any issue tap these guys that give me horrible trouble easily. Its the style of play.
Some general rules of thumb for fighting a bjj guy are very simple. First, keep distance. A bjj guy needs to grapple with you to take you down and submit you. This means you need to hope you are a better striker then he is, and that your body movement is better then he is. Keep circling, and maintaining distance. When you see his level change circle out with strikes. Next when he finally gets the shot in you need to maintain your balance and control his head. This could mean using a wall for support, sprawling, some kind of ninja like rooting. Whatever you do you need to prevent the takedown. A great way to do this is to stuff with a sprawl and push his head down hard. The body goes where the head goes. Deliver strikes and escape.
You are going to find it hard to do any joint locks. Bjj guys are smart about joint locks and they know how to move to escape them and use your attempt to their advantage. To effectively use a wrist lock on them is going to be very hard, you will have more success with armlocks, but you are giving them something to hold on to. This is usually all they need to take you down. I have very little success with wrist locks until I have a dominate position on the ground. Usually the guy just lets go or moves though the wrist lock.
This that will probably not work. Finger locks and breaks. I have broken fingers and toes and in competition usually do not notice right away. In a street fight the attacker is not going to be swayed nearly as easy as a competition. So there is even less likelihood that a finger break is going to matter. Pinches and pressure points are also very low percentage and more the often will just expose a limb for a bjj guy to lock. If you do get taken down it is probably going to be over quick, but if you are mounted there are a few things you should never do. Punching or pushing on the person will only get you armbared. Pulling on them will also expose arm locks. Rolling over will get you choked out. Your best bet is to try to swim though the rain of punches and trap an arm while hipping up to keep them off balance so their strikes are not that hard. Hopefully this will let you roll them over your shoulder. If no strikes are involved then you want to keep your elbows down on your sides with your hands protecting your throat so they can not use their legs to walk your arms up over your head. However if you are on the ground and you do not tons of sparing time on the ground, it is probably over. Your best bet is to just cover up the best you can and beg.
So if you are really worried about a bjj guy, you need to spend some time defending takedowns. This means getting real judo, wrestling, bjj, etc guys to try to take you down in a fully resistant environment. It is easy to stuff a takedown in kata. It is a lot harder when the guy can vary his approach based on your shifting weight and defense. But if you can prevent takedowns, you can nullify most bjj. Then its just a matter of dealing with his strikes. If he is a pure bjj guy, then that won't be much to worry about. However most bjj guys I know also train in boxing or mauy thai because they want to be mma fighters.