Any answer would be pure speculation.
Joint wills that provide for the property of two separate people in one instrument simply aren't done (not truly never, but almost never).
N.B. Sometimes the term "joint wills" is used to refer to separate instruments (usually one for one spouse and one for the other spouse) prepared by the same person and prepared and executed at the same time with mirror image or related provisions prepared as part of an overall estate plan rather than as a single instrument that deals with the rights upon death for two testators. In contrast, a single instrument that is a joint inter vivos trust (i.e. a trust created during life rather than at death) that provide for the property of two settlors (usually spouses) are common in community property states - but the formality requirements for inter vivos trusts are different than the formality requirements for wills.
There is therefore no case law grappling with the issue presented by this question (the validity of a half-holographic joint will). It would be a question of first impression in pretty much all of the common law case law. And, there are reasonable arguments for any of the possible outcomes, so there is no way to predict how such a case would be resolved.
Usually, in cases of first impression, an exhaustive analysis of all of the facts that would otherwise be arguably irrelevant is undertaken, and the judge would do what seems most just under those precise circumstances.
The $500 they saved by not using an attorney or witnesses probably resulted in litigation costs of $50,000-$100,000 for their heirs.