A mutation is miscopying of heritable material. If you want to demonstrate that any such miscopying is random you're going to have to show that there was no cause. We know of many causes of genetic miscopying, but if we see an example to which we can't easily assign a cause it is not justifiable to insert "random." It is simply that we have almost certainly failed to detect the cause. It is far more reasonable to assume that there was probably a cause that we haven't been able to detect than to throw up our hands and declare that it was random.

In an odd way this reflects the attitude of some religious believers who automatically insert God into any gap of understanding we happen to have.