Fingerprinting codes based on the marking assumption provide reliable security against collusion attacks, but lack resilience against channel errors such as symbol erasures or other forms of distortions introduced by transmission over noisy or insecure communication channels. This additional source of distortion errors can be addressed by relaxing the marking assumption. In this paper we examine the restrictions and limitations on the code construction in terms of accusation errors, alphabet size and the distortion errors under this weaker form of the marking assumption, also deriving a theoretical minimum lower bound on the code length of q-ary fingerprinting codes. We provide the formulas for applying already existing binary symmetric Tardos codes under the weaker form of the marking assumption along with numerical results proving the tightness of the derived bounds. We show that binary symmetric Tardos are of asymptotically minimum code length under the relaxation of the marking assumption