If you look at a cancer textbook (eg. Robert A. Weinberg's The
Biology of Cancer), you'll find that by definition, a tumor
arises from tissues normally found in the patient's body.
There's a great deal more to it than just that simple statement,
but given the context of the question, I think that answer
should suffice. In writing, "...tumors growing a tooth,
hair...", I think you're talking about teratomas. These contain
"normal derivatives of all three germ layers". These arise
naturally from cells "...typically found in the human body..."
Cancer is a process where mutations in a single cell transform
that cell into something that is by definition not "typically
found in the human body." But a human cell transformed by
mutation into a tumor (benign or malignant) is never (to the
best of my knowledge) going to magically become a cell from
another species or a very distant ancestor (ie. something that
is not "typically found in the human body.").