Did our Ancestors Stumble From Night Paddocks to Grain Agriculture?

Did our ancestors stumble upon grain agriculture through paddock grazing?

Many grain crop ancestors exhibit fur-zoospory. In other words, many wild relatives of grain crops are adapted to burlike dispersal, forming spiny seedheads that tangle in livestock, etc. fur so that the seed is carried enmeshed animal’s coats to distant grounds to grow.
Night paddocks can protect herded animals from non-human predators. Burlike fur-zoospore  seed might be inadvertantly sown into night paddocks rendered fertile by livestock manure built up over the night stays of the animals.
A livestock rotation among night paddocks could induce grazing down of competitors, fertilizing with manure and seeding with large-seeded grain relatives, all to yield grain-like harvest after a seasons’ growth. Rotation among paddocks could help interrupt livestock pest and disease cycles.
Perhaps early nomadic gatherer-pastoralists noticed better wild grain relative yields where night paddocks were the year before, then tried sowing paddocks after grazing.

One way to check whether this happened is to see whether it is happening among current mixed pastoralists-agriculturalists now.