Just a thought... would purple-leaved strains fare better or worse in areas of intense sunlight?
The purple pigments -- anthocyanins -- are UV protection (much like our suntan response), and might reduce leaf burn.
On the flip side of the coin, their darker color might cause such increased temperatures as to increase leaf burn.
There are many annuums with this foliage color, and a few chinenses (Mata Frade, CGN 21500 and Fidalgo Roxa, for examples). If you tried some of each species, you could have a fascinating thread to start, once you have observed results.
I'll speculate wildly, and guess that the semi-wild chinenses will probably fare better than most. If they weren't bred for ornamentals (like most purple-leaved annuums), then those plants are purple because that's what works for them in their natural habitat.
Your location, California, ranges from (approximately) 32-42° N. Latitude whereas Mata Frade's range (for example) is something like 15 or 20° Latitude (South) from the equator. Unless they have partial shade, or a much lower elevation, they're getting more intense sun than your location.
All other things being equal, i'd assume this strain would have greater resistance to intense sunlight than most.
I have a feeling that a shade-cloth awning is probably more useful then my casual guesses, but a comparison between green and purple-leaved plants alone might be useful. A further comparison between domesticated ornamental purple-leaved annuums and Brazilian wild purple-leaved chinenses might yield results more conclusive