A versus an - We are struggling with the use of a and an

I know when in doubt defer to what the physician prefers.  But suddenly we have one doctor replacing "an" with "a," and is just doesn't sound right.  I was always taught to us a when followed by a consonant and an when followed by a vowel. Apparently this is incorrect, the rule is a when followed by word that "sound" like a consonant and an when followed by words that "sound" like a vowel.  See the rule below:

1. Citibank is a MNC Bank
2. Citibank is an MNC Bank

The correct sentence is number 2.

The Rule

Use “a” when the following word begins with a consonant sound; use “an” when the following word begins with a vowel sound. What matters is how the following word is pronounced, not what it looks like. In the example sentence, “MNC” begins with a consonant, but it begins with the sound of the vowel “e,” since we would pronounce it as “em en see.”

What is your take on this.  Bottom line I will give the physician dictating what he prefers, but he is the only one in the 43 physicians in out pathology department making this distinction.  I've been doing this for 35 years and never encountered this.