OK, let me break this down Barney-style for you.
Is the word "president" followed by a name? If it is, then it is a proper noun and it is capitalized.
Is the word "president" not followed by a name? If this is the case, then it is a common noun and not capitalized.
I don't think I can make it any clearer than this.
Follow the rules or not. It's up to you. They are still the rules.
Now that you have stated the rules properly it’s no problem to follow them.
It’s a bit above your Barney-level to explain that your first attempts to state the rules entirely skipped the context necessary to avoid multiple meanings.
But if it makes you feel better to put the blame on me for not mind reading your intent then, by all means, do that.