"While" in this sense doesn't have a time implication; it means "despite the fact that", or "accepting the fact that", or simply "although".
The two examples you give aren't ideal, as the second clause is insufficiently contrastive. These examples would reflect the more usual context:
1. While they have talked many times, they have never really understood each other.
— which means: "Although they have talked many times, they have..."
2. While it's true that The Simpsons isn't as good as it used to be, it's still worth watching.
— which means "Although the Simpsons isn't as good as it used to be,..."
All the best,
Student or Learner