This thinking implies that a lack of a degree makes one unworthy of consideration for employment.
You are correct that his statement could be read two different ways. You read it that anyone without a degree is instantly eliminated, where I think of it in terms of a stack; the degrees are at the top of the stack for first consideration, and the non-degrees are at the bottom, which is likely to never be reached simply due to the vast number of applicants who do have degrees and are thus going to be considered first.
Aside from helping to prove my own point, where your would-be refutation falls short is that while having a BS is evidence that a person may be motivated, it "does not constitute proof" that one is motivated or (pick your adjective).
Again, you are correct. I should have added a BS from an accredited university and/or an institution where the employer has had a positive history of hiring useful candidates from. A BS constitutes proof that the individual met the standards of the particular school he went to, which may or may not match the standards of the employer. This is why having a wide variety of extracurricular activities and previous employment on a resume is important, because it makes your package even more convincing.

Not hiring a non-degree candidate may be a hasty generalization or it may be based on past experience. It's difficult to convincingly berate employers in general for ignoring non-degree candidates, because their choice whether or not to do so is entirely dependent on their experiences with such candidates as well as the demands of their particular environment.