The problem with that pronunciation is the syllabification. It should be a·po·pto·sis, not a·pop·to·sis. The pt consonant blend is pronounced as a single consonant (as should other consonant blends like pn). English speakers find this sound very difficult to pronounce such consonant blends, so the tradition in English has been to treat the p in words like pneumonia and ptosis as silent, which I can't really say is less correct than pronouncing the blend as two separate consonants. Moreover, ptosis is a medical term which is generally pronounced in English TOH-sis, so it makes sense to me to pronounce apoptosis consistent with that.
Ultimately, though, none of these other issues is anywhere near as important as not pronouncing the initial vowel long, for the reasons I stated above.