Another thing, difficult gymnastic movements are not general fitness. General fitness is being able to lift heavy stuff off the ground, push, pull, and carry weights, etc. not walk on hands, swing on rings, or do back-flips.
Also, whoever you've seen with a very strong deadlift but no chin-ups is either not very strong at deadlifts, or are a professional powerlifter with a bodyweight of 300lb+. I've never met anyone who has a good deadlift but can't pull themselves up. By the way, pull-ups and dips are great exercises, it's just that if someone is starting from zero, it is often beneficial to focus on the core lifts only. Once those are stronger, assistance work like pull-ups can be added in.
In terms of reps, 1RM carries over to other rep ranges. Who do you think can do more 135lb deadlifts: a person with a 185lb 1RM deadlift, or a person with a 405lb 1RM deadlift? Like Rippetoe mentions in his article, increasing maximum capacity lets you perform more work at a lower capacity. Unless you are doing something that requires minimal force production for a long amount of time, such as long distance running, having higher peak strength makes it easier to do.