Hmmm... well, the DRK buttons don't bother me at all. The bulk of this stuff was "custom made" for 1st SS and, IIRC, a few other SS units that had been in Italy (16th SS for example). The SS farmed out the work to cottage industries and/or concentration camp labor. If they found DRK buttons in great supply they would have used them, I have no doubts about that. It could also be that someone replaced a lost button after the war with the DRK button.
If I'm going to get fussy about the buttons I'd look at the one under the collar. If that's plastic then it's not original since the Germans didn't have plastic buttons. Metal and pressed paper were the most common ones by the end of the ware, but Bakelite is entirely reasonable as welll.
If this is a fake it is a damned good one. The cloth looks to have been unused when it was made into the jacket. And after it was made was worn quite a bit. The wear pattern seems to indicate this.
What I'm not familiar with is the general construction of Italian camouflage material jackets. This certainly isn't a standard Wehrmacht or Waffen SS cut.