There are manure spreaders that are much simpler than the high-tech injection system shown in that document you linked to. Something as simple as a cart and a person with a shovel or fork, or something a bit more automated, like a large fertilizer drop-spreader.
The main idea of the injection machines is that you don't spread half of the nitrate content of the manure in the air or rivers, without tilling the land. The picture you posted seems to just spread the manure on top of the land, I think.
Yes, under some conditions, more of the nutrients will be lost when manure is applied to the top of the soil. If the soil is healthy and the manure is spread out continuously over space and time (ie, by cattle on a pasture), loss is not usually very large. When copious quantities of manure are applied to land at one time (like when a barn is cleared out after winter or when someone gets several truckloads delivered all at once), the loss and pollution can be serious.
Timing a bulk manure application so that it is not right before a heavy rain will go a long way to cutting down on the volatilisation and runoff. Applying it to a healthy soil ecosystem, in amounts that the system can deal with is another management factor that reduces loss and pollution.
When the earthworms and insects in a soil have been wiped out, the loss and pollution from manure can be serious because these organisms cannot reach out and pull the resource down into a soil. If a soil is left undisturbed and gets periodic doses of manure, the earthworm population will increase dramatically. Even though 'no-till' and 'low-till' practices can conserve soil in some ways, in their high-tech agricultural forms, they usually involve more agricultural chemicals, and often the use of discs or chisels ... less erosion than regular tillage, but still not necessarily a healthy soil. Studies in Africa have shown when ag chemicals (like anti-parasite meds given to livestock) wipe out the dung beetle, manure will sit on the top of the soil in one place, burn the grass, and is more likely to leach away ... this does not happen in a healthy system when the microfauna break up the manure and distribute it throughout the top layer of soil.
Chickens can be mixed in with larger grazing animals, and the chickens not only control the flies that breed in dung heaps, they also help break them apart and distribute the material. On the pastures around me, wild birds come in and perform a similar function without an invitation from the farmer - there is a niche they can profit from, they see that there are resources free for the taking.
I cannot make a blanket recommendation for every type of possible situation... different climates, different soils, different amounts of manure will influence whether a manuring practice is efficient and beneficial, or wasteful and polluting. But I don't believe that the high-tech methods are generally necessary; the farmer with 640 acres and a feedlot operation may think they are a good solution because he can clear out a lagoon and apply it to his fields in a day or two and be done with it. I believe a permaculturist can develop a decent strategy to apply manures that relies on simple technology and working with the ecosystem.
Couple of years ago i've put down fallen leaves on no-till land and then manure on top, then leaves again. In spring there was great peat-like stuff. I guess this doesn't hurt the ground water and air, leaves does a great job "eating" all the manure.
For beds, I have used my pitchfork to make lots of holes or sometimes pulled back a bit on it to just loosen the soil lightly. Manure added on top and then watered in or a liquid sprayed heavily would easily run down those holes.
Doesn't a disc just slice open the soil? I would think you could run one over a large area and then go back and add the manure on top to allow it to flow down in.
On the border of Zones 5 & 6 on the last 2 acres of what was once a large farm. Flat, flat and more flat!
To prevent manure run off, my mother would predrill trash cans with ½ holes in the bottoms and sides. Then she would dig holes around her garden and place the trash cans into the hole. Then the cans were filled half way with horse or cow manure and then top with water. The tea would slowly leak out into the soil, feeding her vegetable crop. The lids were put on top to cut down on any smells, grandkids and animals playing in them and to prevent evaporation. She would refill the cans once a week with water or when ever needed. The cans would last for years and as they rusted away the tops and lids stayed intact while the bottoms added iron to the plants.