Tesla's explanations ring true to me. That scope picture actually shows both traces cross 0 together. the difference I see is magnitude not time and phase shift.
Adrian I assume you agree that AC can supply linear loads? So if your dam was to only supply 200,000,000 amps of heat across simple carbon resistors the load and voltage would be in phase? only if the load is inductive or capacitive would a phase shift occur between the voltage and the current. Yes I know this is not a real world case as most grids are inductive and current lags the voltage. Any load sharing is related to the capacity of the sharing device and a 100 amp solar array is certainly a higher impedance than the 200 MA dam. Load sharing is simple Ohm's law if the load is 100 ohms, it is 100 ohms to both sources the voltage created in the inverter and the dam must be synchronized to cross 0 at the same time with neither leading or lagging the other in the example of real power only. so the base is the grid and we must sync all input sources to the grid at the location they are interconnected. which ever source has the higher voltage and lowest internal impedance will deliver the amps. Now if my entire load is within the capacity of the inverter then I would want the output voltage to be higher than the grid but not much higher, just enough that the 1st 100 amps comes from my source rather than the grid. As we reach the maximum current output of the inverter it's internal impedance rises a little as the voltage sags a little so that once we tip over it's output capacity any excess demand comes from the grid.
I can tell you it is possible to parallel many generators of many sizes but as soon as one gets out of sync it drops off or quickly becomes a load or fault. In sync definitely means crossing for 0 volts happens at the same instant. How many voltage sources are on the same North American Grid? Thousands! If they are connected together they are in sync and the inverter of DC sources must sync to the same grid.