I have read different explanations for inflation pressures: that the tire's inflation is determined by several factors for optimal traction, rolling resistance, heat tolerance, load rating, etc. But lower pressures don't necessarily translate to more contact area and a "softer' inflation doesn't mean you will get better traction with a lighter weight load or in slippery conditions, either. Lower pressures can actually cup the contact patch and burden the edges, while offering less traction and contact. Optimal inflation will open the tread to its most effective formation and broaden the contact patch. I'm guessing that recommended pressures may not necessarily relate to the added weight of the front end, but I could be wrong. My Mustang is heavier by far in the front end, but all tires get the same air pressure. My Stinger AWD is heavier in front than a RWD, but the same inflation is recommended for both models. Or, I could be full of shit and your explanation could be right.
Additionally- I've read the air in the tire doesn't "support" the weight. Oddly, the tire hangs on the rim and it's the sidewall that carries the weight. Inflation only expands the tire to its proper dimensions to facilitate this function.