I should specify-- I had read that the SS in Austria investigated him, publicly exonerated him, and allowed him to emigrate to safety.

I have written about Dr Bloch here.

There was no backlash as at the time of Bloch's emigration, the official policy was to push the Jews out of Germany/Austria, not to kill them. Therefore, his emigration was perfectly in line with Nazi plans. An estimated 250,000 Jews emigrated from Germany between the coming to power of the Nazis and the start of the war.

Also, Hitler did not publicly state that the doctor was a good man, he stated this privately.