Can my dishwasher lacking a 'high loop' cause it to fill with dirty water, even if it happens hours after I last ran it?
Not having a high loop in the drain line could be causing this issue. I'm guessing that your drain connects into your disposal. In that situation if you don't have a high loop when you run your disposal or empty water from the sink on the disposal side it could back up into the dishwasher.
It's easy enough to set up a high loop if there is enough slack in the drain line. Simply loop it up as high as possible. Be careful not to kink it. You can attach it to the inside of the cabinet wall or under the countertop with a clip or zip tie.
Some local codes require the installation of an air gap vent on dw drain lines for the above reason. You might want to check. If one is required it would be a good idea to have one installed. That will solve your problem.