I have the Sawyer Mini and use it home and abroad and use Aquaventure tabs if the water looks very doubtful.
It is not so much the risk of getting ill, but the risk of getting ill thousands of miles from home with resultant medical expenses, delay, cost of change of flights, etc. Why risk all that by not treating the water.
Coming across a dead sheep, or similar, higher up after sourcing water is not a myth. I have a come across a dead deer twice in streams in the Scottish Highlands.
However most gut incidents come from poor personal hygiene, pooping in the woods, not washing hands effectively afterwards and then eating.