GCBHM, no doubt this "instructor" got some facts wrong. In a mobile home park, I would even be pessimistic on using #6 birdshot. I have seen articles endorsing the use of #6, to prevent penetration through sheetrock interior walls in home defense scenarios. By the same token, use of such a load would almost need to be at "contact" distances, as that small shot loses energy and velocity quickly, making it ineffective at any moderate range.
Buckshot is more effective, and retains velocity and energy to longer distances, but as has been mentioned, when you have multiple projectiles released with each round fired, you are "accountable" for each one. This always was a factor, when breaking out the shotgun, as a cop. As mentioned, pattern what you use, to know what your "maximum" distance to engage a suspect with your scattergun, to insure "all" of your pellets will remain in the intended target.
That's one reason the "Patrol Rifle" became popular, using frangible ammunition. When you have 8-12 .33 caliber lead balls exiting your barrel for every shot of 00 Buck, anyone within probably 75 yards down range could be in danger. In a rural environment, it's not normally a problem, but in an urban environment, it is most always a concern.