As Scilling pointed out in another discussion thread:
the 'an' is frequently pronounced as an unstressed 'a' between consonants"
The current speaker does this quite freqently, and for me it is sometimes a challenge, whether the intended meaning is "the", "his", "her" or "their".
I presume, that this is later part of the advanced training sessions.
Definitely a fact....a meaning his and an meaning the are pronounced exactly the same throughout the course. If an meaning the, for the purpose of instruction, it should be accentuated, not distorted, over emphasised by pronounced in a manner so it is clear that the word An is being used and not A