Why does "is" replace "has"?

They are not interchangeable. What happens is that the contracted forms of has and is sound the same in sentences like:

He's been doing that for years.

(He has been doing that for years.)

and

He's not a doctor.

(He is not a doctor.)

In your example, I think he might have said:

This song's been written by XXX.

(This song has been written by XXX.)

I believe he is saying "has" and leaving off the "h". It might sound exactly like "is", but it's actually not. Americans also often leave off the "h" in words like "him" and "her" when these words are not accented.

"has" is used for the perfect tenses(present perfect), and shouldn't be replaced by "is", which is only for the simple tenses. It is not correct.