According to sources, while the majority of the footage used in the trailer is from the Top Gear USA series that Microsoft does have to rights to use through their partnership with them. Two other sources of footage were also used which were sources from Clash Productions and Turn9. Microsoft had licensed video from Clash Productions, and apparently Clash Productions were fans of the Turn9 stuff and working to help promote it; but in the end it was a miscommunication between the parties where they thought that they had the rights to use the Turn9 footage, but apparently they did not.
In the end, Microsoft and the folks at Turn9 are staking out the issue, which could be a bit complex as apparently the two actors in the video are Screen Actors Guild (SAG) members, and this could complicate the issue. It sounds like a lot of things were just lost in the translation and that no one that was acting in bad faith.
We suspect that they will sort it out, and it still is a great promotional video for Forza 4. Everyone involved could have likely done without the drama surrounding its release, however.