I'm not really sure he repented of being a Nazi.
Then he shouldn't have even gotten any sacraments. This is what I don't get: he was repentant and participated in the life of the church, but was refused funeral service? That wouldn't make sense.
What we don't know is the status of the priest who confessed this man and what his secular beliefs were. Priests are not robots, dispassionately conducting services and granting absolution. Perhaps he was a Holocaust denier or noted revisionist who was known to Church authorities.
This would not be the first case where a church burial was denied to avoid placing the church in scandal. I know of local situations where an Orthodox Bishop, when consulted by the pastor, denied a full church funeral for disciplinary reasons.
The Catholic answer to the deceased' s relationship to God here would be akin to an Orthodox one. If he died in communion with the church, having been confessed, absolved and having received the Eucharist, the absence of a burial ritual will not impact his standing at the Final Judgment. That we leave to God. But if the public burial were to be used by some as earthly "proof" of the church's "approval" of the deceased, given his lifelong public denial of responsibility for his acts during the war, I have no issue with the Vatican's decision.
This is a war crimes issue, not a Holocaust one and it involves sensitive issues regarding the complicity of elements of the Catholic Church in Preibke's crimes.
"Erich Priebke (29 July 1913 – 11 October 2013) was a German Hauptsturmführer (Captain) in the SS police force (Sipo). In 1996 he was convicted of war crimes in Italy, for participating in the massacre at the Ardeatine caves in Rome on 24 March 1944. 335 Italian civilians (among them 75 Italians of Jewish ancestry) were killed in retaliation for a partisan attack that killed 33 German soldiers. Priebke was one of those held responsible for this mass execution. After the defeat of Nazi Germany, he received help from a bishop stationed in Rome and fled to Argentina on a Vatican passport, where he lived for over 50 years.
In 1991, Priebke's participation in the Rome massacre was denounced in Esteban Buch's book. In 1994, 50 years after the massacre, Priebke felt he could now talk about the incident and was interviewed by American ABC news reporter Sam Donaldson. This caused outrage among people who had not forgotten the incident, and led to his extradition to Italy and a trial which would last more than four years." http://en.wikipedia.org/wiki/Erich_Priebke