A nice question.
Suppose a painter paints a scene with a person in it. Apart from very special circumstances, we wouldn't take this to be a matter of the painter telling us that the event really happened and the person depicted was really there. It might be that a real person is depicted who really was in the place pictured. But that's not how paintings are ordinarily intended, and it's not how they're ordinarily understood. Calling the painting false because what it asks us to imagine never really happened would be a bit like saying that the Sherlock Holmes stories are false because there was never any such person as Sherlock Holmes.
Of course, a painter could use a painting as a way of conveying information intended to be factual. I take that to be the point of your example. And in many cases, some aspects of paintings are intended in just that way. Suppose a portrait depicts a blue-eyed person as having brown eyes. Depending on the larger story, this might be a genuine inaccuracy in the painting. We could certainly say things like "the painting gets it wrong," and no one would be confused.
The case of the doctored photo is a good one. Pictures are often used as a way of conveying information, and they can be used deceptively. I can lie by using a picture. That means I can use a picture as a way of asserting a proposition that I know is false.
So why not say that in such cases, the painting is false? We could, I suppose, and there could even be a set of conventions governing the use of the words "true" and "false" when applied to paintings. That said, it's not hard to see some reasons why we don't do that. Close enough for present purposes, the content of a proposition is definite. And in typical cases, which proposition a sentence is used to assert is unambiguous. "Schenectady is in New York" is a good example. There's very little ambiguity, if any, about what proposition someone is asserting when they use this sentence, and so the question of whether the sentence is true or false has a clear answer. The semantics of sentences like this is reasonably clear and the way in which they can be combined with other sentences to produce yet other sentences more complex truth-conditions is clear. That's not so for pictures. We can use sentences to assert disjunctions ("or" statements), negations, conditionals, etc. What sort of picture would say that Mary has one or two children? Or that if Mary gets to work late, she will be fired? We can dream up ways of doing this, no doubt, but we'll mostly do it ad hoc.
Or for that matter: which features of pictures would we take to be part of what's asserted? Again, in particular cases we could have ad hoc rules that settled the question. But when pictures are used to make assertions, it will be a matter of some features of the picture being used in this way, even though other features that equally well could have been used to make assertions aren't.
To tie all this up, one important difference between pictures and sentences is that sentences usually have a reasonably clear syntax and a reasonably well-settled semantics. (I don't mean that the theory of syntax and semantics is well-settled; I mean that in practice we can generally agree on the structure of actual sentences, and we can generally agree on what they do and don't mean.) This allows us to talk about truth and falsity in a precise and structured way. Pictures often have rich representational content, but it's a considerable stretch to say that there's a full-blown syntax and semantics for pictures. This doesn't mean that we can never apply terms like "false" to a picture, but pictures are very different from the sorts of things to which we paradigmatically apply words like "true" and "false."