The "right" pronunciation depends on what you take for reference. If you're treating the word as an English one, the woman is right - English doesn't allow this sort of initial cluster, and spelling-wise it's well-established that some initial consonants are mute (see e.g. "knife").

And, if treating the word as a Koine Greek one... odds are both are butchering the word so much that [pə] wouldn't save the day. Even the man is likely pronouncing it as [pə.'tɒl.ə.mi]; the Greek word would be more like [pto.le.'mɛ:.os], or [pto.le.'maɪ̯.os] with a really conservative pronunciation.

… although, I guess any pronunciation will be wrong because the actual name was “Πτολεμαίος”, so if you wanted a correct transliteration you would have to use “Ptolemaious”

Regardless, Joey is still closer to the correct pronunciation.

How about the breathtakingly wrong Latin pronunciations?

Veni Vidi Vici