Problem with 'that' clause

It shames us as a nation that a freedom fighter has to scrape a living singing on the streets in his twilight years.

No: the that clause is not an objective complement.

This is an extraposition construction where the dummy pronoun "it" is subject and the that clause is an extraposed subject; the extraposed element doesn’t give the meaning (reference) of "it" but serves simply as a semantic argument of the VP.

The non-extraposed counterpart would be:

That a freedom fighter has to scrape a living singing on the streets in his twilight years shames us as a nation.