Which is correct? I was born on Friday or I was born on a Friday

[alvask]

Recently I heard an opinion that when you do not use an indefinite article before a day of the week then it is the same as if you were saying "this" before that day of the week. In other words when you say on Friday you are referring to the most recent Friday or to the Friday on this week. Please let me know whether the above is true.

Please confirm that the following is right:

We went to see Swan Lake on Friday / We went to see Swan Lake this Friday
We are flying to Rome on Friday / We are flying to Rome this Friday

What day of the week did the Titanic sink? - I think it was on a Monday.

Never open a fish restaurant on a Thursday. It's bad luck.

When were you born? I was born on a Friday.

 

[Barb_D]

I confirm.

(Not that "When were you born?" is usually answered by a day of the week! You'd usually give a date. But in answer to "What day of the week were you born?" you'd say "on a Friday" not "on Friday.")