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They [the players] may not show these cards [their hands] to the other players or communicate what they have.
In other words... booyah.
As for the stipulation for Mind, I'm not sure I'd attribute much to that. Eon later created a game called Dune in which the Emperor's alliance power was to allow him to give spice to other players -- but everyone can do that already. This text was just added as a reminder, not to imply some earlier rule was a mistake.
I believe the Mind text serves a similar purpose, and it looks like they did well to add it since so many people don't remember the initial secrecy clause, haha. Plus, as you pointed out, this was in every edition but the Eon edition (that I've played, at least -- Eon, AH, CEO, and FFG), and only the Eon edition had the rule enforcing card secrecy, so it was pointless in that edition to have the extra Mind text, thus explaining why it was added in later editions.
I've pointed this rule out to many a long-time Eon player in my comparatively short Cosmic career (I've been encountering aliens only since the Avalon Hill edition, though I did at one point play the Eon version a few times), and it's surprising how many do not remember this rule ever existing. In fact, I don't think I've ever talked to anyone who knew the rule.
I could see why some people would like to ignore the rule, but my personal preference is to pretend that the rule still exists in all forms of play. I don't like being able to plan a deal. That seems somehow cheap to me. And I don't like being able to say what's in my hand, because cards change hands often, and it would annoy some players if someone with a big yap gave away a card they were hoping to bluff with or whatever. Of course, you can lie, but I prefer to save that kind of treacherous play for Dune. And perhaps even worse, some people play games with complete honesty.
Just to clarify, I know the rule isn't in FFG's version, but I house rule it in.