Not enitirely so. My wife was a German citizen and got naturalized. In order to regain her German citizenship, she would have to renounce her American citizenship. By becoming an American, she lost her German citizenship.
From Nationality Act (Staatsangehörigkeitsgesetz, StAG)
Section 25 [Loss of citizenship on acquisition of a foreign citizenship following due application for the same; approval of retention of citizenship]
(1) A German shall lose his or her citizenship upon acquiring a foreign citizenship where such acquisition results from an application filed by the German concerned or his or her legal representative, whereas the represented person shall suffer such loss only if the qualifying conditions for application for release from citizenship apply as stipulated in Section 19. The loss under sentence 1 shall not take effect if a German acquires the citizenship of another member state of the European Union, Switzerland or of a state with whom the Federal Republic of Germany has signed a treaty under Section 12, sub-section 3.
(2) Citizenship shall not be lost by any person who, prior to acquiring foreign citizenship following their application for the same, received written approval from their competent authority for retention of their citizenship. Where an applicant is ordinarily resident abroad, the German diplomatic mission abroad shall be consulted in this connection. The public and private interests shall be weighed up in reaching the decision on an application pursuant to sentence 1. With regard to an applicant who is ordinarily resident abroad, special consideration shall be accorded to the question of whether he or she is able to furnish credible evidence of continuing ties with Germany.
Germany has eased its citizenship controls significantly in large part to accommodate the Turkish guest workers who have stayed for generations. That said, relatively few have been naturalized and when the Germans discover they have retained their Turkish passports/nationality, they take away their German citizenship.