Actually, she has not said "people must trust us". The only part of her speech in Davos with the word "Vertrauen" (confidence, trust) translates as follows:

We need to make another attempt at a European constitution process...We have seen/realised by the failed referenda in France and the Netherlands: If we are to have success we need Citizens who have trust/confidence in such a Europe.

If Britain is against a European move that counts in Germany as an argument for it being a good move.

"The sooner Britain gets out of it" is a state of mind that finds more and more supporters in Germany.

Wolfgang