There's a funny thing that happens when you look at more and more advanced orchestras. Across the board, the level of musicianship and technical skill increases among the players in the ensemble. This has a side effect in that more advanced orchestras need less and less information1 from the conductor in order to play together, in part because section leaders and concertmasters/mistresses are more capable of leading other members of the orchestra from their desk.2
However, technical proficiency in conducting does not necessarily increase in the same manner. At the lower levels it does, certainly, but there comes a point where a conductor can be renowned for any number of aspects related to conducting, not just technical proficiency: his or her rehearsal technique,3 overt expressiveness, a cult of personality, or simply a preference to leave time up to the ensemble and exert his or her efforts on expressive aspects of the music. What you will see with truly excellent conductors is that they possess both the skill to supply any information necessary (including time), but also the awareness to tell what information is necessary at the present moment.4
But unfortunately, in many cases it comes to be that ensembles simply don't trust their conductor to give them accurate time, and instead they form a habit of watching the first violinist for the downbeat.5 There is no reason this has to be the case -- if a conductor is proficient in communicating time effectively with gesture, it is much easier for everyone in the ensemble to simply watch him or her (they do stand upon a podium, after all).
I do hope no one is teaching young orchestra players that it is "correct" to play "after" the beat of the conductor -- that is entirely missing the point, which is to play in time with everyone else in the ensemble, through any of the methods described above. An ensemble does not play in time by everyone making an independent guess of how long after an ictus the beat is supposed to be.6
So, just to reiterate on the question in case this point got lost in the above discussion, but you are on the right track in thinking about musical discourse between the conductor and ensemble. To a degree, that's the Karajan approach: this well-known TED talk relates a story of a flute player asking Karajan when he was to come in, since it was so unclear from his gesture. The answer was "Play when you can't stand it anymore!" But by the same token, it's easy for this to become an illusion and bad habit if the issue is just that the conductor is not prepared to lead effectively--and that's really what all of conducting is about.
1. In which Leonard Bernstein leads the final movement of Haydn Symphony No. 88 primarily with his face, and little else.
2. As the story goes, some famous conductor, upon hearing the brass come in sloppily at one point in a symphony, stops and says "Together, with me please!" The first chair trumpet player leans forward and turns his head to give a look to the rest of the section. Next time through, the conductor conducts in exactly the same way, but somehow the section was able to play together... So who do you think they were following?
3. Rare footage of Karajan in rehearsal. Not known for his specificity of gesture, but absolutely a brilliant genius of a conductor.
4. Nearly every example of Carlos Kleiber you will find is a masterclass in conducting. A perfect example of giving the ensemble what they need, and none of what they don't. (And is the ensemble behind his beat?)
5. The dreaded opening of Beethoven Symphony No. 5. The concertmaster nearly falls out of his chair!
6. Another, likely apocryphal story: a conductor whose ictus was so nonexistent that the ensemble members simply agreed amongst themselves that the beat would be placed whenever the baton reached the fourth button down on his shirt!