Yes, Salty, you can catch this stock trail from Happy Isles - go past that rockfall exhibit/educational loop trail and head upstream. There's a nice bridge further up. You're right, hikers are not supposed to be on this one. I discovered it coming down the JMT - we "accidentally" wandered past the merge down to the Vernal Falls toilet at the bridge. I don't recall seeing any signs posted up there, but I remember seeing a sign down at the rockfall loop about no hikers or bikes. I guess someone could get "lost" and end up on that trail. The stock cowboys might not take kindly to it if you meet up with them.
Not sure if this alternative is the original JMT. It's quieter for sure, but you miss some views of Illouette Falls and Yosemite Falls that you see on the paved highway. We've also seen bears occasionally on the regular route, which is always fun.