This is quite a hard question to answer fully, so let me try to break it down as I see it, step by step.
1) You are right to think about this in terms of semantics. I don't think trying to analyse syntactics is going to help you much. Furthermore, I don't think a grammatical analysis is even particularly relevant, though it is of course tied to the semantics.
2) It seems to me that the problem here is your understanding of the meaning of treat someone to something. In your mind, it seems that the meaning of treat someone to something is the same as give something to someone and give someone something. Although they are similar in some ways, they are not exactly the same. The dictionary definition is not helping you in this regard. The problem with the dictionary definition is that it is incomplete.
You are right that in both patterns, there is a performer and a beneficiary. However, it is the precise nature of this relationship that differs. Let's now look at the difference in detail.
GIVE
The core sense of the verb give is that there is an exchange of an object from the performer to the beneficiary. In terms of semantics, give is what is called a three-place predicate. That means that there must necessarily be three parties (or 'arguments') involved. These three arguments have the following semantic roles:
1) agent (the 'giver' or what you referred to above as the performer)
2) recipient (the 'givee' or what you referred to as the beneficiary)
3) patient (the 'given' or the object that goes from/to.)
TREAT
The verb treat is different in two main ways.
Firstly, unlike give, there is not necessarily (although there may well be) an exchange 'from/to'. Look at this example:
For your birthday, I'll treat you to a day at a health spa.
In this example, I'm not really 'giving' you anything in a literal sense. I know it seems like the day at the health spa is a gift (it is) and that you are the beneficiary of my action (you are) but there is no literal exchange of the health spa from one place to another. We commonly use treat somebody to something in this way: to mean that we pay money to allow somebody to benefit. In your sentence I gave him an apple, we understand that there was an exchange (what I'd call a 'transaction') taking place. In the sentence I treated him to an apple, there is no such transaction. Out of context, the most likely interpretation is that I merely paid in some way for the apple, from which he benefited.
Secondly, in terms of semantics, treat is only a two-place predicate (agent and patient only). This is where the grammar ties in, and is precisely why you cannot say *treat somebody something, using an indirect object. The fact that treat is only a two-place, not a three-place predicate, means two things:
1) It is therefore not necessary (although it is usual) to mention the thing that the benefiter benefits from. (You can just say I'll treat you without mentioning 'what', whereas you cannot say *I'll give you.)
2) In terms of semantics, in the sentence I treated him to an apple, him is the patient. This is very different from the sentence I gave him an apple, where him is the recipient.
