The point is that property owners (the ones granting the allotments to keep the poor quiet) are the ones forbidding the use of the allotments for commercial gain.
Again, allotment holding is distinctly not property ownership. So it's strange to hold this up as an example of property ownership causing oppression when it's the opposite (unless you consider e.g. a feudal lord's position as being "property ownership", which it really wasn't). The point of the claim that property rights create freedom is that a model in which even the poor get to own land outright is far better than the model of sharecroppers/tenant farmers/serfs.
Allotments are very much not property rights (or at least, they're a much more limited form of ownership than land titles); they harken back to the tradition of common land. Property rights advocates argue that enclosure and sale of land (that could be used freely by its owner) is a better model. So I don't follow your point at all here.