Without the full nodes rejecting the non signaling segwit blocks, the miner would not have decided to forked. Without him forking, the market would not be able to determine the outcome.
So essentially your proof of power of full nodes is: full nodes have power over miners, because full nodes have power over miners.
No, seriously. You talk about a "proof of power" and you assume in your proof what you need to prove

In fact, you *don't even need a UASF node* ! If miners decide to fork with a minority segwit chain, and they do this long enough, then this particular minority chain will be 100% segwit signalling. If you force your core node to connect ONLY to these miner nodes and refuse to have it connect to any other peer in the network, then after a while, your node, not learning about any other block chain on the network, will see as the only chain, one which has been signalling segwit at 100% for long enough, and will ACTIVATE segwit. From that point on, your node will reject non-segwit blocks, and you can now connect it to the whole network, it will refuse the longest chain as invalid, and continue to consider only the segwit minority chain.
Now suppose that I play a joke. I launch 8000 UASF nodes (nodes don't cost much). The minority of miners fork. I let them mine for a while. And now I switch off my UASF nodes. Bam. They have been mining on a short chain. All transactions gone. They've been wasting their hashing rate because some dude started many nodes and they believed it mattered.
IF miners think that it is in their advantage that there is a fork, they don't need to wait for UASF nodes. And if they think it is risky to leave the main chain, then they will still think it is risky, even if many nodes appear that signal being a UASF. Again, what matters to them only, is that they can get listed on an exchange as a separate coin. Whether you run your node in your basement or not doesn't matter. So the decision to split depends not on that node. It depends on what they think the market will do, and if they should take the risk to leave the main chain.