You need "of" in standard English.
Consider the following sentence:
The monster (that) I saw in the cave
was hideous.
That is a relative pronoun: it refers back to the monster (the antecedent), and it introduces a subordinate clause of which it is itself the object, that I saw in the cave (the relative clause). We could use what here:
What I saw in the cave was hideous.
As you see, what has swallowed its antecedent: the relative pronoun what always does that, because it always includes an antecedent. If the antecedent must be specified, what is impossible. Apart from that, it functions just like that or which. In your of sentence, if I were to replace your what by a that, it would look like this:
I can't confirm all of [the things]
that she said.
I was forced to supply the antecedent that was hidden within what, because that requires an antecedent. I made something up, these things. This all works fine. However, consider your sentence without of:
*I can't confirm all what he said.
If I replaced what, I'd get:
I can't confirm all [the things] that
he said.
This might look all right, but think about the antecedent: what is it here exactly? The problem is that the antecedent is not just the things, but also all: "what did he say? he said all the things; what can't I confirm? I can't confirm all the things". The adjective all is part of the antecedent, which is why it too should disappear if you use what:
I can't confirm what he said.
That is why your sentence without of doesn't work in standard English. There might be dialects in which this happens regularly, though. Normally it should be one of the following constructions:
I can't confirm all he said. (That is implicit.)
I can't confirm all of what he said.
I can't confirm what he said.
Context is important here:
If a piece of steel or a piece of salt, consisting of atoms one next to the other, can have such interesting properties; if water—which is nothing but these little blobs, mile upon mile of the same thing over the earth—can form waves and foam, and make rushing noises and strange patterns as it runs over cement; if all of this, all the life of a stream of water, can be nothing but a pile of atoms, how much more is possible? If instead of arranging the atoms in some definite pattern, again and again repeated, on and on, or even forming little lumps of complexity like the odor of violets, we make an arrangement which is always different from place to place, with different kinds of atoms arranged in many ways, continually changing, not repeating, how much more marvelously is it possible that this thing might behave? Is it possible that that “thing” walking back and forth in front of you, talking to you, is a great glob of these atoms in a very complex arrangement, such that the sheer complexity of it staggers the imagination as to what it can do? When we say we are a pile of atoms, we do not mean we are merely a pile of atoms, because a pile of atoms which is not repeated from one to the other might well have the possibilities which you see before you in the mirror.
Emergent properties of even simple systems can be remarkably complex, as a complexly arranged pile of atoms, our emergent properties may be even more amazing than water patterns.
Best Answer
It's technically (almost) correct, but obviously a pathological case for the fun of it. Moving the prepositions into their "standard" positions and adding the appropriate pronouns gives:
That is, from back to front:
The from out of bit is incorrect, as you can tell if you try to rearrange the sentence to involve both from and out of: it should be either from (the book) or out of (the book).
Though you should usually avoid doing so excessively, it's perfectly correct in many cases to shift a preposition to the end of a clause and omit the pronoun (such as which or whom) that would otherwise be involved:
There's a long history of prescriptivist grammarians considering it incorrect to end a clause with a preposition, but there's such massive precedent in favour of doing so, and it's so common in ordinary speech, that you can't legitimately make the claim that it's outright wrong. And for certain examples, as the above, it sounds so awkward and stilted to use the “correct” form that that form cannot possibly be the truly correct one.