I know we've been through this whole vowel this before, but this is my take on it.
Please correct me if I'm wrong because I'm no Greek expert!
PnguinTrax, I think they mean that Alpha itself is a vowel, not that Alpha ENDS in a vowel. You used the examples Alpha and Beta. Although they both END in vowels, only Alpha is actually a vowel, hence the difference in pronunciation. Beta itself is a consonant. So the rule works not with "a letter ending in a vowel", but rather when a letter IS a vowel.
Don't need to go into this whole thing again, but I hope that clarifies things a little.
Oh, and RainMan--that was very interesting! I never heard of "hybrids" when discussing Greek/English pronunciations before!