I think this picture is deeply confused. In particular, it is a mistake to think that plants have "interests" in the same sense that people do. When I say that it is bad for a person to be belittled behind his back, I do not mean this in anything like the sense in which it is "bad for" a plant to lack water. For when I say that it is bad for plants to lack water, this is just a coded descriptive claim: I mean nothing more than that certain descriptive facts hold. To think that plants have interests like ours (that merely differ in their importance, not their fundamental nature) is like thinking that evolution has "aims" like ours. To avoid conceptual confusion, we should recognize that biological teleology is merely metaphorical -- a convenient shorthand with no metaphysical bite. The real thing requires a mind.
So I think there are two very different senses in which it is bad for a person to lack water. There's a minimal sense in which it's bad for us in exactly the same way as it is bad for plants, i.e. it is against our biological interests. This purely physical fact would hold equally of our zombie twins (since biology supervenes on physics). But there's clearly a further sense in which we are harmed that our zombie twins are not. It isn't just that harms to us matter while harms to zombies don't; it's that the kind of "interests" we have in common don't essentially matter (to either of us). What matters are our normative interests, where this means something quite different.
To bring out the distinction, note that it's straightforwardly absurd to think that one could be "harmed", in the biological sense, by facts that never affect your internal, biological properties. This suggests the following argument:
1. Given the (biological) sense of "interests" in which plants have interests, we have exactly the same interests as our zombie twins.
2. It's obvious that a zombie isn't essentially harmed by such biological epiphenomena as secretly being insulted (in such a way as has no further consequences).
3. But there's an important, normative sense of "interests" in which a person may be essentially harmed by secretly being insulted. (Such claims about wellbeing at least aren't obviously false or incoherent, the way they would be if 'harm' meant 'biological harm'.)
4. So: there's an important sense of "interests", had by people, that is different from the sense in which plants, zombies, etc., have "interests".
Because the two kinds of "interests" can come apart, we can see that the "single sense of interests" view will entail false moral conclusions. For example:
1. If anything is against an organism's biological "interests", death is.
2. If an organism has moral status, then its [biological] interests are morally significant.
3. So, if an organism has moral status, we must consider its painless death to be morally significant.
This conclusion is false. We can coherently take animals to have moral status, without considering their painless deaths to be bad (so long as they are replaced, perhaps). We might think that only pain and suffering are bad for animals, they can't be deprived by death like persons can. Since this view is perfectly coherent, we must mean something different by "interests" than the biological sense, when affirming premise 2.
One may then ask: what, exactly, is this normative, non-biological sense of "interests" that applies to us but not to plants? Simple. Our normative interests are simply what is desirable for our sakes. [Update: see the comments for clarification.] Nothing is desirable for the sakes of plants. That is to say, we never have (intrinsic) reason to desire something for the sake of a plant. (What does a plant care whether it survives or not? Plants have no "perspective" from which things might be considered better or worse, in the normative [reason-implying] sense.) But sentient creatures are different. We typically have reasons to desire some things and not others, for a person's sake.
This brings us to my argument that it's incoherent to think that an entity is harmed (in the relevant sense) but that this somehow lacks [even prima facie] moral significance:
1. The relevant sense of "interests" is conceptually tied to desirability, i.e. reasons for desire, for the individual's sake.
2. Weak benevolence thesis: A reason to desire X for S's sake is, ipso facto, a prima facie moral reason to straight out desire X.
3. So, if S would be benefited (harmed) by X, this is a prima facie moral reason to straight out desire X (not-X).
Now that's just to say that X is prima facie good (bad). So facts about interests (in the relevant sense) necessarily have moral significance. That is, it's a mistake to think that plants or embryos have interests, in our sense, but simply don't matter morally. It would be morally arbitrary -- a violation of weak benevolence -- to think that something is desirable for S's sake, yet not (even prima facie) desirable tout court. What could possibly justify neglecting S's interests from the start like that? (Retributivists think that we have reason to want bad things to happen to bad people. That's fine by me. It's just a case of further reasons overriding the prima facie ones we had for wanting good things to happen to them.)
You can't reasonably deny moral standing to beings that have normative interests. I should emphasize that this isn't a mere tautology: "normative interests" means normative-for-them; it's a substantive moral claim that this entails normative-for-us. But it's also an obviously true moral claim. So while you could deny it, you surely shouldn't. Once you've determined that an entity has been harmed, in this sense, this suffices (given the truth of weak benevolence) to settle that this fact matters morally.