Arduino -> SRF02 (Fake-Mode Problems)

First: use code tags for your code parts, else the tag parsing on the server may omit some code.

The problem is that I get wrong distances as result.

May I guess: your result is about 10-15cm wrong?
The transmission of the range command takes approximately 300us which translates to about 10cm. If there's another delay in the communication that I've missed it may be more. The datasheet explicitly states that you are responsible for the synchronization of the two sensors if used this way.