The maximum entropy principle is a cornerstone of FRAME (Filters, RAndom fields, and Maximum Entropy) model considered at times as a first-ever step towards a universal theory of texture modelling or even as "the inevitable texture model". This paper disputes such opinions. That a wealth of exponential families of probability distributions is deduced from the ME principle is well known for decades. The ME property by itself in no way leads to an adequate probabilistic description, and to model a particular texture, specific limitations have to be imposed on signal statistics. Frequency distributions of outputs from a bank of linear filters (the second FRAME's cornerstone) are hardly the only choice outperforming all other alternatives. The paper points also to other hidden drawbacks of FRAME.