Their population problem is apparently bad enough that the bodies of their population are pressed up against the sides of their Enterprise facsimile as well
...But a project of such importance would be in a populated area anyway - not to mention it would have to be close enough to the government building that the discrepancy in beamdown coordinates would not be blatantly obvious. Probably buried right beneath the building, actually.
OTOH, Gideonites would have quite an interest in the project, and spectators would be a natural phenomenon! Having a one-way mirror briefly fail isn't all that unexpected, either. Note that all the people behind that mirror were
spectating, rather than just wandering around like in the government building.
Except you're perfectly aware that conditions such as these did not exist in the overwhelming majority of American and European cities and do not exist there now; nor have they been common to nations and regions that were NOT heavily urbanized, nor do they persist OUTSIDE of urban population centers.
Incorrect. Twenty people per room was fairly standard for the early age of industrialization in the major cities of Europe, and remains so in many places where migrant workers are a prominent phenomenon (examples can even be found in my own extremely sparsely inhabited Finland today, although these tend to involve illegal or "grey area" activities and a degree of secrecy).
In rural areas of all but the warmest climes, a typical dwelling consisted of but one winterproof room, and having a family of three or four generations stuffed in there for months at an end (and occasionally having sex, because there was no reason not to) was a very common phenomenon.
I can't fathom why you would think otherwise.