If the reporter hasn't received a list of the things tested-for-and-negative, from a representative of the competent institution that did the testing, that's
definitionally 'hearsay' in a legal context. Even in a lay context, I'd say that's hearsay from the perspective of both the reporter, and the article readers (albeit not from the perspective of the mother who received the claim directly herself).
Your point about only finding what's tested for is valid, and when imprecise assurances are passed from unnamed-medical-tech, to grieving mother, to reporter, it's especially likely relevant details get either filed-off, or embellished. A kind but nondefinitive mention, "we didn't see any evidence of intoxicants" could morph into the far-stronger claim, "they said they tested but found no trace of drugs or alcohol".
Note also the UC Davis burn center is more-than-an-hour by medivac from Black Rock Desert. If Mitchell was effectively lost before he arrived (even if not "called"), would any toxicology even be run? It wouldn't change the treatment or prognosis.
Also, at least one info page from a peer institution (UCSF) about toxicology screens does not include LSD, MDMA, or many other hallucinogens in its otherwise-detailed list about what might be detected: https://www.ucsfhealth.org/medical-tests/toxicology-screen
When I first saw the vague reference to "friends from Switzerland" in the article – without names or any reporting followup to speak with these last pre-incident witnesses – I even thought it might be a sly euphemism for a large LSD dose, given that substance's roots in Switzerland. But seeing that Mitchell had resided in Switzerland, seeing some friends from there becomes the far more credible interpretation.
Your summary lessons are great advice!