All characters get certain default skills (to 1/2 or 0 depending on edition) if they can be reasonably expected to have learned them.
All marines could therefore have vacc suit to its default level.
Since vacc suit skill can be used to wear battle dress then yes, all marines can wear it.
True. But, there is a difference in a character with Vacc Suit-1 wearing BD and a character with Battledress-1 wearing BD.
VS allows the basic use of BD as a vacc suit only. BD skill is need to operate BD to its fullest, including all its weapon and other systems that are not found on a regular vacc suit.
What is a "Battledress"? It's a powered vacc suit with several systems attached to it--including weapon systems.
So, VS will get you into the suit and safe from the elements but it won't allow you to us all the advanced tech tacked onto the suit. You need BD for that.
All Marines
are expected to be riflemen however, so be careful of your analogies.

If one considers that battledress is just as much a weapon as an actual, well, weapon, than perhaps a case can be made. Just food for thought.
I
almost mentioned this in my original post, but I thought it too obvious.
I believe I read an interview with MWM one time where he discusses the cutlass. He explains that he still trained with bayonnet, even though the weapon was considered obsolete, and that became the main reason Traveller marines always got cutlass.
Of course, in the Traveller universe, cutlasses do a have a use--knives and swords are much more useful in a zero-G invironent (no recoil and the ability to kill the enemy by cutting his hose).
I don't think I have to be so careful about my analogies that I made in my previous post about Battledress, though, Vargas :devil:. Have you seen the cost of BD? It's way to expensive to be a standard weapon/piece of equipment that everyone is trained to use (especially if they never have a need for it).
No, not all Imperial Marines are trained with BD.
If so...it would be in the rules, the way cutlass is (besides all these other, better, arguments).