I would too.
There seems to be a lot of "issues" around this, and SCOTUS cases, etc.
Generally, I think they'd have to show need, for treatment. I suppose law enforcement could get a warrant too. (And there have been big fights over that too...like in DWI cases). It's so all over the place, and may even vary by state jurisdiction. Google search:
when can a hospital perform a drug test without consent - Google Search
As you point out, a drug screen in treating a person acutely ill is not uncommon. It requires no special consent, although if a person is able to communicate, they can refuse to provide a sample for one, much as they can decline any other medical procedure, test, or treatment. Results obtained may not be turned over to law enforcement in the absence consent by the individual or a court order, as is true with your privacy rights to begin with.
THC remains in the body for a significant period of time. The presence does not necessarily indicate very recent exposure. It's why if you need to take a drug screen, for say work, you need to stop a few weeks prior if you're a regular user. A problem for law enforcement is a positive test for THC does not establish say driving while under the influence or impaired, they need a field sobriety test. It's not like blowing an alcohol level of 0.08. So in this case, the presence of THC on a drug screen does not establish a clear relationship to the illness, although one's spidey sense might be thinking about toxic exposure to something. But given how common cannabis use is these days, it will not be at the top your list until you've excluded other causes.
Not all patients admitted to THC use. Saying you don't believe them isn't enough to say "yeah, it had to be related to that and they're lying", especially at the beginning of reports about this respiratory illness. Once that was sorta correlated, the cartridges involved may well have not been available to testing by a lab. That NY State Dept of Public Health identified the presence of Vitamin E acetate was fairly prompt under that circumstance.
The fact that early reports all had one thing in common, vaping SOMETHING, made it reasonable to start looking there. To jump to an early conclusion of "it's THC street stuff not Juul or e cigs" actually would have been bad science. From a public health standpoint do you really want to eliminate the possibility that an adulterant or contaminant didn't enter the nic e juice supply line? When a containment was identified, focus did turn to looking for that and other contaminants across all the cases to establish whether in fact it was that or a combo with something else.
It was the politicians who chose to jump on it like rabid dogs thrown a piece of meat to give them cover to make the soccer moms happy. Besides, when you see pictures of kids on ventilators holding up signs "Don't Vape" can you not have some political reaction?
The fact is, we still have no direct evidence the Vitamin E acetate is definitely the cause. The odds are super high, but it doesn't mean you one, stop testing for anything else, and two, you still need some sort of model to see if the respiratory damage is reproducible, most likely in animal testing as giving it to human volunteers at this point wouldn't be all too ethical.
If blame is to be placed, I'd look at the media feeding off the story and politicians capitalizing on it for their own gain. Could the CDC have released the information earlier? Maybe, although there were comments made earlier that the media didn't pass along as being as significant. After all, drug users getting sick isn't as sexy a headline as kids dying from vaping. Now that data has firmed up, they are being more proactive in narrowing down their recommendations and direction of the whole inquiry.