Emphasis the other way, I think; the idea is that a yielding surface offers more grip to an unguligrade than a non-yielding one, whereas a digitigrade would be happy with either.
Having read the basic description of team penning on wikipedia, I’m more confused rather than less. If the cow that freaked out had its number called, then “the contestants couldn’t pen it obviously” doesn’t make sense. By calling that cow’s number, wasn’t that cow thus designated as precisely a cow the contestants could and indeed should be penning. 
Or do you mean that the escaped cow was not one of the designated “target” cows?
I suspect that the difficulty cows have negotiating stairs has a lot to do with their lack of familiarity with them.
Most dogs go up and down stairs easily, but I fostered a GSD adult rescue that had never seen stairs before and she was very unsure and reluctant to use them. Down seemed to be more difficult for her than up.
Penning isn’t an imitation of rounding up cattle from the range and getting them into a corral, it’s an imitation of all the sorting and shuffling cattle into their correct boxes that happens after they’ve been rounded up. As a sport, penning is done in a large arena with 30 head of cattle milling around. There’s a small pen set up at one end of the arena, the goal is to get the target cows (and no others) into that smaller pen. I think Senegoid was saying that the cow climbed the arena fence and was trotting away through the parking lot. It’s the cow equivalent of a foul ball, I suppose, only no-one knew what the rules were to handle it.
I always interpreted the original statement to mean ‘it’s easy to get cows to go up stairs, but then you can’t get the #@#% to go back down’, not ‘cows physically can’t walk down a staircase’.
To clarify that a little bit: Perhaps you are confused as to the order in which the events happened:
The announcer calls a number (0 to 9) at the beginning of the round.
Then the three contestants (who are working as a team, not as opponents) have to chase down the three cows with that number and chase them into a pen.
As they were doing this, one of those three “target” cows climbed over the fence and left the arena completely. So there was then no way for the contestants to pen that cow. So they forfeited that round and essentially got disqualified, through no fault of their own.
On the other hand, there was another round, with a different team of contestants, where everything broke just right for the players. As the contestants approached the herd, three of the cows broke away from the herd and headed away, toward the pen end of the arena – And they were just the three cows with the “target” number. The contestants got them penned in about 10 seconds.
I commend your pee-pee spotting skills, which are surely greater than mine.
(Cow can refer to the species as well as sex btw, and often is.)