Why is the floral biodiversity of grazed grassland higher than that of mown grassland?
I think you may have covered the answer in your question... but here's my take;

The 'mowing' occurs at a distinct time-point and is highly destructive and uniform, so the selection pressure is very high and only highly competitive species that are fast to grow and reproduce will be successful.

As you point out, animals will defecate and naturally fertilize the land, thus favouring growth. Other favourable factors in an agricultural environment will be that the 'mowing' will be much less uniform; the animals may favour one plant over another - so a plant that is not eaten by the animals will continue to grow and reproduce, whereas in the mowing environment this plant would not succeed; this will allow various other species to succeed where they would not in the mown environment. Also, depending how many animals are in the area the height of the grass may be higher overall, so slower-growing plants could grow enough to reproduce.