Whether LLMs memorize their training data and what this means, from measuring privacy leakage to detecting copyright violations, has become a rapidly growing area of research. In the last few months, more than 10 new methods have been proposed to perform Membership Inference Attacks (MIAs) against LLMs. Contrary to traditional MIAs which rely on fixed-but randomized-records or models, these methods are mostly trained and tested on datasets collected post-hoc. Sets of members and non-members, used to evaluate the MIA, are constructed using informed guesses after the release of a model. This lack of randomization raises concerns of a distribution shift between members and non-members. In this work, we first extensively review the literature on MIAs against LLMs and show that, while most work focuses on sequence-level MIAs evaluated in post-hoc setups, a range of target models, motivations and units of interest are considered. We then quantify distribution shifts present in 6 datasets used in the literature using a model-less bag of word classifier and show that all datasets constructed post-hoc suffer from strong distribution shifts. These shifts invalidate the claims of LLMs memorizing strongly in real-world scenarios and, potentially, also the methodological contributions of the recent papers based on these datasets. Yet, all hope might not be lost. We introduce important considerations to properly evaluate MIAs against LLMs and discuss, in turn, potential ways forwards: randomized test splits, injections of randomized (unique) sequences, randomized fine-tuning, and several post-hoc control methods. While each option comes with its advantages and limitations, we believe they collectively provide solid grounds to guide MIA development and study LLM memorization. We conclude with an overview of recommended approaches to benchmark sequence-level and document-level MIAs against LLMs.