Decision scientists have grown increasingly interested in how people adaptively control their decision making. Researchers have demonstrated that parameters governing the accumulation of evidence towards a choice, such as the decision threshold, are shaped by information available prior to or in parallel with one's evaluation of an option set (e.g., recent outcomes or choice conflict). A recent account has taken a bold leap forward in this approach, suggesting that adjustments in decision parameters can be motivated by the value of the options under consideration. This motivated control account predicts that when faced with difficult choices (similarly valued options) under time pressure, people will adaptively lower their decision threshold to ensure that they make a choice in time. This account was supported by drift diffusion modeling of a deadlined choice task, demonstrating that decision thresholds decrease for difficult relative to easy choices. Here, we reanalyze the data from this experiment, and show that evidence for this novel account does not hold up to further scrutiny. Using a more systematic and comprehensive modeling approach, we show that this previously observed threshold adjustment disappears (or even reverses) under a more complete model of the data. Importantly, we further show how this and other apparent evidence for motivated control arises as an artifact of model (mis)specification, where one model's putatively controlled decision process (e.g., value-driven threshold adjustments) can mimic another model's stimulus-driven decision processes (e.g., accumulator competition or collapsing bounds). Collectively, this work reveals crucial insights and constraints in the pursuit of understanding how control guides decision-making, and when it doesn't.