Yes, the sentence is technically ambiguous.
Consider this similar construction: "She redecorated the room by adding a new chair and new curtains on the window." Like your example, we have two nouns linked with "and", and then followed by a qualifying phrase. Would you understand this sentence to mean that both the chair and the curtains are on the window? Probably not. I think most readers would understand that to mean that the curtains are on the window and the chair is is not. The chair is probably on the floor.
To understand a sentence, we often have to combine a knowledge of grammar with knowledge of the context and apply common sense. As Andrew illustrates with the elephant in pajamas joke, many sentences are theoretically ambiguous if we just look at the grammar, but people routinely apply common sense to understand the meaning. Many jokes are based on pulling the rug out from under that common sense, and re-interpreting a sentence to a meaning that is consistent with the grammar but is not consistent with our common sense.
BTW lawyers love to play word games like this. There are many court cases that are all about debating exactly what the words in a law or a contract mean, just what nouns a restrictive clause applies to, etc.