To put it simply... it's your story. You get to choose.
There are a huge number of grey areas or areas that can potentially be expanded upon in the canon, especially if you're working from the games (as I assume you are, because you mentioned them specifically). Now, the games don't allow for anything like plant manipulation, but only because it's not possible to use environmental attacks in a game where battles take place in a blank arena that has very little impact on the actual fight. This means that you are effectively left free to make it up: it's a grey area, and no one will challenge you on it if you choose to make it so.
However, it has to make sense. Like Foxrally, I don't think it makes sense to make a Parasect control plants - it's only a Grass-type because there's no equivalent type for fungi, it being a parasitic mushroom controlling the brain of a hapless insect. I'd query it if you decided to give it the ability to control plants.
Torterra, to take the other example Foxrally gives, would be fine. It has a tree growing on its back, it can use Frenzy Plant, which certainly looks like plant manipulation to me - I wouldn't see anything particularly canon-breaking in that. For that matter, let's add in Venusaur, Sceptile, Meganium and Serperior, too - the other users of Frenzy Plant.
I could go on, but that seems kind of pointless. I wouldn't say that all Grass-types can control plants, no, but with a little thought, you could easily find enough of them that you could justify giving this ability to. I suspect most of them will fit the bill - I can see the Victreebel line doing it, for instance, and the Tangrowth line, and so on. If you wanted a Trainer character whose battle strategy relied on manipulating plant matter in the environment around them, you could definitely find six Pokémon for them to use. (Although I personally find giving six Pokémon to a Trainer makes their team somewhat bloated and unwieldy - but that's a digression. Stop it, Cutlerine. You're beginning to ramble.)
Anyway. I hope that makes your position a bit clearer. You're free to make it up, as long as the reader can look at what you've written and think, "Well, yeah, I can see that happening... yeah, that kinda makes sense to me."
F.A.B.