But I don't think the same standard applies. ...I just need to raise the specter
By that rationale, the theory stated below by Magicsound is just as valid as yours:
Some unknown person (whose initials could be E.W.) sneaked into the lab wearing an invisibility cloak (without opening the door of course). Then he compromised the experiment by touching the lead in front of the spectrometer with a refractory wand containing 90Sr, and left, again without opening the door.
When it come to these kind of supposed refutations, I think it is necessary to do more than just "raise the spectre". Otherwise we'd be here all day, slowly descending into a rabbit hole of weirdness.
For instance: Given the "signal" graph, (and knowledge of the scintillator programming) we can calculate the number of counts* received. Then, knowing the length of measurement 7, and the half-life of Strontium, we could calculate the minimum size and weight of this alleged free-floating particle... Which should give an understanding of whether it would actually float around the lab, or just fall to the floor.
It might not be completely conclusive, but at least it demonstrates that we are not just waving our hands and pulling rabbits from hats, as it were.
* Or is the 'count' axis just arbitrary? Either way, I'm sure you get my wider point.