I am on the side that says the farmer didn't plow the field. I guess you could say he took responsibility for it, which isn't the same thing. I guess a counter argument that some would make is that the farmer didn't plow the field if they didn't pull the plow themselves (or to a silly level: if they didn't plow the field with their bare hands). They just pressed the right pedals while sitting in the tractor. I am not sure I have a good argument either way, but a farmer plowing a field with a tractor is physically involved during the whole process, and it feels more fair for them to say that they plowed the field, for the simple fact they weren't doing anything else during the process other than constantly controlling the plowing machinery.