I think I found your error in your thought process. This is wrong:

"If he does the first option (take a loan and distribute to himself) he has no net income (the truck is a write off),"

has nothing to do with the Net Income. Debt decreases equity and Distributions decrease equity, too. Even doing Both will not change income.

The purchase of the truck either outright or by debt, results in a new asset and the depreciation, making the Asset total change 0 and in your example, the depreciation coincidentally makes the Net Income 0. That doesn't change for whether there is distribution in addition, for whether the truck is bought outright or there is debt. Take just that first part: New asset, fully depreciated, and happens to be the same amount as the Net income (which is part of equity and becomes the RE). Once you state that "depreciation expense happens to = net income" then the rest is all Balance Sheet activity.

So, using the bank funds to buy the truck outright simply is Asset = Asset, or No Change to the balance sheet. Taking the funds as distribution is Reduction in Asset = Reduction in Equity, or No Change to the balance sheet. And, taking on debt to buy the asset decreases equity, so No Change to the balance sheet.

You cannot be Out of Balance, here. You seem to be posting something to the wrong place or forgetting about "the other side" of it.