As with many words, the meaning of "width" depends on the context. I would say your answer is given by the Oxford's definition. If you notice, two different definitions are given, the first assuming the object is upright and with width meaning the side-to-side distance. The other definition is orientation independent, and in my opinion better because of it, and it simply states that for a 2 or 3 dimensional rectangular (-prism), he width is the shortest dimension's distance. This is a common challenge when you use words that have a colloquial meaning and a technical meaning. Other examples are the word acceleration, in physics slowing down means you are accelerating, in fact, your speed may not change at all yet you may still have an acceleration; in a colloquial environment, acceleration is associated with increasing one's speed only. A person's weight prompts different answers from different people, in general you'd expect an answer in pounds or kilograms, a physicist would probably say, "assuming it's on Earth, the weight is", followed by a number of Newtons.

The way I address it with my own children is to explain to them the more nuanced definition, trying not to openly undermine the teacher but rather expanding on what they were taught on the first place, when it is possible. My approach has always been explain to them as if they were scientists, and build up your answers until they seem to have enough or are not engaged. Discussions about the color of the sky, or the meaning of pi, with 4 year old children can be wonderful experiences for you and for them and allows them to question what they learn at school and expand on it.