That depends partly on the context, partly on personal preference/habit.
Speaking for myself, if I'm emphasizing the indefinite article (for instance, to inquire as to the extent of the generic nature of what I'm describing) — such as when asking for clarification, as in "Do you mean if I kiss ɛɪ frog or this frog?" — I'll tend to pronounce it as ɛɪ. Otherwise, ə would be the usual pronunciation in most other situations.
I agree with you that the divergence of the pronunciations in your example sentence seems strange — I can't seen any obvious semantic reason for it. In that sentence, I think most people would pronounce it as ə in both cases.
The most likely possibility that occurs to me is that the announcer was reading from a script without concentrating properly, and therefore inadvertently ended up stressing the first 'a' incorrectly.
(Incidentally, I have yet to unmask any princes using this method of investigation.)