That's not black-helicopter crazy. I say this because:
i) until not that long ago, experiments were conducted with looser controls than now, especially during the Cold War era. They were generally, I believe not intended to cause harm, but they also did not go through layers of independent review.
ii) some dangerous experiments have been publicly admitted, with unfortunate consequences for those involved. LSD experiments on unknowing subjects, electroshock, and the famous syphilis trials. This shows that in some cases it was experiments were done on people without their consent or knowledge that they had been experimented on. While there were not many of these, it would be naive to believe that they do not exist until declassified and publicized
iii) and finally a factor I believe is underestimated: a combination of arrogance, ignorance and "whoops who'da thunk that?". Unintended consequences. Examples of possibilities which I believe are reasonable, not nut-case theories:
A bio-agent test is intended to cause a few sneezes and test only if the powder disperses to the population, but some percent of the public becomes violently sick, someone gets dizzy and falls off a subway platform. None of the healthy subjects they tested the "harmless" substance on had such a reaction -- they didn't bother considering the full range of people and effects involved.
Or as you suggest, a substance beleived to be mostly benign is prepared at a remote test location where bio-weopons are developed. It isn't thoroughly tested and contains a contaminant, either from the lab or the isolated environment where the lab is located. It's somewhat like driving on an unfamliar road at night after just a few drinks. One doesn't intend for the multi-fatality crash to ensue, and indeed you could do this 20 times before "wooo--- what happened" spoils your day. Only in this case the experimenters are watching the car not in it.
I'm sure there are other non-conspiracy whacko events which might have occurred.
Personally I believe Nature to be far trickier than our inventions, but it's not impossible that human shennangans had a role in tickling nature to show its claws. Note that Royal Free Hospital disease appears to have no connection to any such experiments in the US.