Vermeer and Hans Holbein are well known for having used the camera obscura, but other masters' use of it is not known. I think that it's existence is no reason to particularly suppose its use by them, just as today's existence of the opaque projector is no reason to suppose its use by most portrait artists, though some do use one.
But the fact is that the skill required to draw a likeness, while not easy to come by, is also not restricted to the domain of the great masters. There are many artists today who are well capable of obtaining accurate likenesses without a projector, as I'm sure there were in the old times. It's just not that uncommon a skill; it's something one can learn, like any skill. I figure some of the old masters probably eschewed a projector for reasons of pride alone, as do modern artists. Especially as it's not something a trained artist even needs.
And, as you mentioned, often work done from photographic reference gives itself away. Probably many feel and felt the same about projected work.
RE your comment about realism now being able to be painted by a machine, that opens a fairly interesting debate, one that is often alluded to on these threads. But it always brings to mind to me Jacques Barzun's comment about how if all the old masters were painting realistically, then how come all their stuff looks so different?
Now I have to go look up that Bill Clinton portrait you mentioned.
A young artist of our acquaintance mixes his own colors ~ and his work looks different from the other students who rely on factory controlled standards.
Fortunately for him he is able to duplicate his color mixes perfectly.
Now, concerning the varnish on those paintings, I'd guess the 16th and 17th century "Masters" used high quality lacquer from the orient, and since they were working in the major European port cities they had access to the very best stuff. Unfortunately, bug based lacquers darken with time ~ someone probably has done a doctorate on the photoactive qualities of some of the animals in the mix.
Which raises yet another question ~ were these guys using a "wash" on their canvas and panels which was "photo reactive".