Different stories on this! It seems Tom got all the permission to shoot since the Finance Ministry is the one who decides, and apparently they have given permission to shoot.
Reuters says:

Cruise film to work around German military site ban

Sat Jun 30, 2007 6:23 AM IST
BERLIN (Reuters) - The makers of a movie about a plot to kill Adolf Hitler said on Friday they had the permits needed to film in Germany despite being declared unwelcome at military sites because its star Tom Cruise is a Scientologist.

Defence Minister Franz Josef Jung has made it clear the filmmakers could not shoot at any military sites if Cruise plays hero Colonel Claus von Stauffenberg, because of his link to Scientology. Berlin regards it as a cult masquerading as a religion to make money, a view Scientology leaders reject.

But the head of the Babelsberg Studios in Berlin, which will handle filming in Germany, said he had all necessary location permits, including for the so-called “Bendlerblock” where Stauffenberg and his co-conspirators were shot after the attempt to kill Hitler with a briefcase bomb on July 20, 1944, failed.

The Bendlerblock is located in what is now the Defence Ministry complex in Berlin. However, part of it is run by the German Resistance Memorial Centre and not the ministry, and Babelsberg Studios says it intends to shoot the film there.

“They have given us permission like they have done for other Stauffenberg films before,” Carl Woebken, head of Babelsberg studios, told Reuters.

The buildings’ official owner, the Finance Ministry, had also given permission, he said. “From our point of view, everything is ready to go.”
Woebken said it was important to film at the Bendlerblock for the sake of authenticity.

A German government official said on condition of anonymity the filmmakers did not have a green light to begin filming at the Bendlerblock. This lack of a green light could complicate the shooting, scheduled to begin next month, he said.

The film, slated for a 2008 release, will be directed by Bryan Singer and Kenneth Branagh will co-star. It is called “Valkyrie” after Operation Valkyrie, the plot’s codename.

Sabine Weber, a Scientology spokeswoman in Germany, said German politicians were attacking top Scientologists like Cruise, one of the producers of the film, to get their names in the press.
“I believe that certain politicians from the Christian Democrats use the celebrity status of some of our members to step into the limelight, that’s what this is all about. They don’t care how much they damage Germany’s reputation,” she said. (Reuters)

On the other hand, I’ve found this story, dated today, saying:

Tom Cruise can’t film at German military HQ, authorities confirm

Saturday 30 June 2007 13:49
Germany’s Finance Ministry confirmed Saturday that Tom Cruise has been banned from filming at a military headquarters in Berlin, but denied this was linked to his advocacy of Scientology.The US actor-director is planning a movie called Valkyrie about the July 20, 1944 attempt to assassinate Nazi dictator Adolf Hitler, who survived the blast with minor injuries.

Cruise, 44, is playing Count Claus Schenk von Stauffenberg, the military officer who led the plot and was executed in a courtyard, close to his own office at the army and navy HQ known as the Bendlerblock.

“This place of remembrance and mourning would lose its dignity if it were to be used as the backdrop to a film,” said Torsten Albig, a spokesman for the finance ministry, which is responsible for the administration of the building.

Germany’s defence ministry had earlier spoken out against the building being used as a location for the film, shooting for which is expected to begin on July 19. (Jurnalo)

It seems the second story isn’t accurate, and it’s logical to believe a more trustworthy news source like Reuters. So I think we can conclude everything will be okay regarding the shoot. If there’s more insight to the story, we will let you know! And if indeed the Jurnalo story is inaccurate, I will delete it from our site. For now I did want to report it, since we’re not out of the woods with all the reports.