Ah, the Hockney theory. Although I wouldn't doubt that the understanding of optical principles may have improved people's refinement of perspective, the camera obscura was never a practical aid for drawing or painting, even when one used a lens (without a lens it would be totally useless). There are plenty of artists today who can draw and paint without using such devices; I don't see why Bourguereau should have been any less capable.
Even though it's possible to photographically print an image onto canvas and then trace over it, which would be a huge step above using a camera obscura, paintings made by such methods generally look horrible. There is no way that a painting produced using a camera obscura would look any better. Indeed, given the practical difficulties of using such a device, it would be impossible to make even a decent trace-painted rendering of anything but the most hard-edged, motionless objects.
If I may offer an analogy, while traditional animators have often used motion-picture film enlargements for design reference, good animators basically never trace it directly. Rotoscoped animation tends to look rather flat, dull, and lifeless compared with animation drawn freehand. Even though rotoscoped animation might be "technically" more accurate, from an aesthetic standpoint it is vastly inferior.
Some people claim the quality of Bouguereau's works proves he must have used a camera obscura. I would claim that, to the contrary, it proves that he did not.
Human beings, of course, have tremendous accuity, but they do not and never did have the accuity of an eagle, and it takes an "eagle eye" (in the form of a 2X or greater lens) to give it to you on a two-dimensional surface.
Almost every experienced artist on Earth can differentate between detail paintings that required the use of a prosthetic and those that didn't. So can you.