Beardsley's not a zoo that brings in the big bucks. I'm not sure how the rest of the viewing for Pampas Plains is but I'm not too surprised that for the rheas- which won't be big ticket animals- they just went with chain link viewing.
STE, I'm guessing the enclosure seen up front is the peccary one, and then you can walk up along a side path to reach the rheas?
You are correct regarding the peccary but not about a side path. There are closer ANGLES but no up close, right next to exhibit, viewing.
At least when I went.