Energy payback is not the same as carbon neutrality. The former only accounts for the economic value within a regional market and ignores externalities.
Just compare the price of a solar panel with the price of coal you'd have to pay for in China. That's the uppermost possible limit of what you could expect for CO₂ emissions if you didn't have to pay for anything else. Just conveniently assume all your workers and other raw materials are free. ;) You can probably buy two tonnes of coal in China for the price of a ~250W solar panel. That gives you about 4000 kWh of electricity. At a 15% capacity factor in China, the same panel can generate at least 6500 kWh in 25 years, even including quite substantial degradation. So if used to offset electricity generation within China, it's neutral after 15 years.
In reality, it's most likely much sooner because you don't need 4000 kWh of coal electricity to manufacture a 250W panel; you have to pay your workers and raw material suppliers instead.
All energy is not created equal. In order to make this calculation in a useful way, one would need to know the amount of carbon emissions per kWh for both the panel production site and ones local grid. And it's actually even harder than that, as one also needs to know if one is lowering base-load generation needs or surge-capacity. Base- and surge-generation are frequently not the same as carbon emissions go.
Consider for instance that you live near the Hoover dam (desert, lots of sun, prime area for solar); your panels might never be carbon-neutral.
Sure, it's complex. Take your example. The Hoover dam sells power into California. So installing solar panels in Boulder City is not that different than installing them in Los Angeles (there would be some extra grid losses in LA). If the Hoover Dam had the capacity to supply the entire southwest it would matter, but it doesn't have that capacity.
There's also the question of whether buying Chinese solar panels makes China more or less likely to convert to solar itself.
Even in a 100%-coal grid, I don't think it's likely that >1000 kg CO₂/kWp is necessary. German manufacturers can achieve 400 kg CO₂/kWp in the still-rather-mediocre German grid.
If energy is the only input to making a solar cell (the worst case) and the cell costs x Wh then the market price can't go below x * ($/Wh), so it pays back when you produced x Wh (thus not buying x Wh from the coal burning power plant) and any energy you produce is both profit for you, and also less total demand for coal energy.
