We're working with a proxy for consumption: net injection. Net injection is affected by weather. Good forecasts make for good guesses of net injection in a relative sense...if any week is forecast to be cooler than average in the summer, and the forecast is correct, one can successfully predict that, in general, net injections should fall below the long term average for that week, and visa-versa. And as you have said, anyone can make those calculation given the injection data available plus weather observations and weather forecasts.
I don't know what happens on the production side, but to suggest that producers somehow collectively decide to throttle up or back production based on weather is probably taking the argument a bit far. Its more likely that they alter production based on price and I would bet that, in any given short period, production is not in fact terribly affected by price unless price declines for a long period below the marginal cost of production. If price rises above the marginal cost of production then you get exploration and well development, and new production comes on stream. The amount of new production then depends on the projected internal rate of return which varies from project to project and locale to locale. Complicated stuff! So, not being an NG economist, I stick with what I know and focus on the consumption side to make my investment decisions. Cheers, CJ