The most obvious is the hay just was too mature when harvested. Early bloom to ¼ bloom should have finer stems that are more pliable, and test in the 20% Protein range. The most obvious reason is the hay is baled too dry and most of the leaves are shattered off, leaving mostly stems. At this point we do not know if the stems are the problem or if it is the irrational, notional, simply difficult to please hay buyer and the animals like the hay just fine. The problem of the "horses" not liking the hay can be due to off flavor or odor. I do hope this neighbor has a collection of hay analysis for you to look at. Too low a protein may mean the hay is over mature. With a mineral report you can look at the mineral analysis to see if the hay is low in P, K, Mg, &/or Ca.
It might be a good idea to collect a tissue sample prior to harvesting and compare it to the hay analysis's mineral report. Personally if these horses are not brood mares, or in competitive training I would feed the horses grass hay. There is more energy in alfalfa than a horse just standing around can burn up in a day. | 
Alfalfa for horse hay
