This question is interesting. Amherst’s letters seem to be clear. The part that doesn’t make sense is that the disease transmission process wasn’t really understood until the work of Pasteur. At the time that Amherst mused about infecting people with small pox blankets there were various beliefs about transmission of communicable diseases, fog and bad air being among them.
LINK TO COLUMN: Did whites ever give Native Americans blankets infected with smallpox? - The Straight Dope
You’re generalizing (as your teachers probably did) from false beliefs about, e.g., malaria. That contact could spread smallpox was very well understood, to the point that inoculation was practiced (at terrible risk) with smallpox long before Jenner’s application of cowpox.
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Since the time of Genghis Khan at least, there was an understand that items in contact with diseases would trigger more diseases. This led to such tactics as flinging dead animals into fortified cities, putting carcasses down the wells, etc. It’s not a new concept at all.
For examples, see this.