The theory of propensity score (PS) suggests that it should only be used for the cohort study because PS matches the "treated/exposed" to the "un-treated/un-exposed" groups. However, cases and controls are the outcomes (not the exposures) in a case-control study. What are the pitfalls if PS is used in a case-control study?
A propensity score isn't just a way of matching groups. There are other ways to use propensity scores - at its heart, its a way to characterize the probability of being exposed given covariates. When this is adjusted for in any one of a number of ways (including matching) you theoretically break one of the conditions necessary for confounding.
The problem with a case-control study is its very hard to calculate a true probability of exposure for the same reason its hard to calculate a true probability of disease: you don't have a whole cohort to work off of, just an unbalanced sample. That being said, there are some articles discussing the use of propensity-score methods in case-control studies. This one might be a good place to start. The main thrust is that they're much less straightforward to use, so unless you have a credible reason to adjust using propensity scores instead of outcome-oriented approaches like including covariates in a model, it might not be worthwhile.
04/03 edit for your comment:
It's not a matter of matching to the exposure or the outcome. In all matching, you're matching on covariates. The propensity score is just a way to roll all your covariates into one composite covariate - the propensity score itself. What you're doing by matching is trying to find cases and controls who had ~equal probability of being exposed for all covariates save for your exposure of interest. Observe that in the SUGI paper you linked, the actual code to generate the propensity score used in the matching is the following:
PROC LOGISTIC DATA= study.contra descend; MODEL revasc = ptage sex white mlrphecg rwmisxhr mhsmoke ... / SELECTION = STEPWISE...; OUTPUT OUT = study.ALLPropen prob=prob; RUN;
That code is modeling your predicted probability of having the exposure (revasc). See Page 2 of that paper.