In short, yes. The hole for the well works both ways; it's a fast track for any surface-level pollutants to get into the groundwater, contaminating it for everyone.
Local law may require barriers to prevent this, such as an elevated concrete pad at the top of the well. This how-to guide didn't mention anything like that. Permits help ensure that important steps aren't skipped.
You should be 100 times more worried about fertilizer runoff into storm drains than some random farmer drilling a well and then ruining it by pouring used motor oil into it.
Local law may require barriers to prevent this, such as an elevated concrete pad at the top of the well. This how-to guide didn't mention anything like that. Permits help ensure that important steps aren't skipped.