Our Versace family sources say they can't believe the current owners of Gianni's Miami Beach mansion -- now the Villa Casa Casuarina -- gave full access to producers of "The Assassination of Gianni Versace: American Crime Story." In particular they're appalled the show was able to dramatize the death scene on the very steps Gianni was gunned down.

We're told Donatella is still devastated over her brother's death and believes Gianni was so private he never would have wanted the grisly murder exploited for a TV movie.

As we reported ... filming began at the now luxury hotel back in May where 'ACS' set up shop for almost an entire month.

The family tells TMZ they didn't sign off on the project and had no involvement in the production, and they feel there are enough inaccuracies that the miniseries should be considered a work of fiction.

Donatella has already said she will NOT watch the show. That said, we're told family friends have already screened the first episode and were APPALLED to watch the horrifying murder.

The family plans no legal action ... fact is, it's virtually impossible to win a case like this.

We have reached out to the Villa Casa Casuarina ... so far no word back.