In Book V of The Histories (Aubrey de Selincourt translation) Herodotus notes:
The Parians, whom the people of Miletus had chosen out of all the Greeks to settle their disputes, managed the business in the following way: their best men visited the place, and when they saw the widespread ruin there they asked to be a allowed to make a thorough inspection of all the land. This they did, and whenever in the desolated countryside they saw a bit of well-cultivated ground, they made a note of its owner's name. Of such farms, however, though they examined the whole Milesian territory, they found very few. After their inspection the commissioners returned to the city and lost no time in calling a general assembly, at which they announced their decision to entrust the government to the men whose land they had found in good order - for there was no doubt, in their opinion, that such men would manage public business as efficiently as they had managed their own. The other Milesians were told to take their orders from the new government.
Are there any other accounts that corroborate with Herodotus on this?
I assume that he isn't referring to the farmers who actually worked the land, but the landowners who owned the farmland. Are there similar instances throughout history where governance was placed in the hands of people due to the upkeep of their agrarian estates?
I know a little bit about Classical Athens so i'll try and answer in that area.
Before Democracy developed in Athens, Public Service was only open to a certain wealth bracket (those making 500 bushels of corn or equivalent) who were eupatridae (meaning well-born). As this definition implies, most of the wealthy at this time were landowners who rented out land to small-holders and so were the majority of the ruling class. This changed as the Athenian Constitution developed, with the wealth-qualification lowering for the archonship (the main administrative role), but still existed, meaning that the farmers still were important political figures (it is important to note that most wealth derived from the land).
After the so-called "Democratic Revolution" in 462/1 B.C., Athens was largely run as a direct democracy, meaning all could contribute at the Assembly (or ekklesia) by speaking. Despite this, most magistrates (a sort of Civil Service selected by lot) and especially the elected generals (strategoi) tended to originate from the wealthy, which, although by this time including more merchants, still was primarily the agricultural class. The classic example will always be Pericles, strategoi and co-instigator of the "Democratic Revolution" who came from the historically powerful Alchmaeonid clan.
The rise of the demagogues signalled the decline of the ruling class as they tended to come from the lower classes.
If someone more well-informed knows anything better, feel free to coorect/add. I'll try and answer any questions tomorrow.