I'm reading a paper that compares different probabilistic models using the log likelihood of held-out data. This is just... wrong, correct? There's no meaningful way to compare the LL between two different models? If I'm correct, what is the right way to do this comparison?
You have to find out what they mean by "held-out".
Usually, the "held-out" set is a validation set, a separate dataset that is used to estimate the test set error. For example, it is useful to estimate the test set error to do model selection on different hyperparameters and/or early stopping*. That is very common because ML algorithms often have many hyperparameters that are not fit during learning (the "K" in K-means, the regularisation coefficient in logistic regression, the number of iterations for iterative algorithms in general...).
However, "held-out" literally means "taken out of" so depending on the context, I could see how the authors of the paper could denote the test set by it.
You can trust the comparison if the authors do not use the held-out set for learning parameters or choosing hyperparameters. That is the right way to do this comparison.
* early stopping can be seen as nothing more than hyperparameter search on the duration of training.