Can longitudinal and cross-sectional studies be "controlled"? I have heard it said that longitudinal and cross-sectional studies are forms of observational studies. 
Why can't longitudinal and cross-sectional studies be considered  "controlled studies"?
By their definitions, I think they can.
 A: Whether data is observational or controlled is not related to the type of data (longitudinal or cross-sectional) but it depends on how the data was collected. The main difference is that in experimental data you have controlled the setting such that you can exclude other outside influences that may affect the outcome - for example via an experiment in the laboratory. If you do your experiment once, it's a cross-section and if you repeat your controlled experiment several times with the same individuals, you obtain experimental panel data.
A: Think about it in terms of an intervention I functioning om some outcome X.
If you have a controlled experiment, you use a (pseudo-)random mechanism, such as a random number generator, to sort the respondents into a control and a treatment group, where only the treatment group should receive the intervention. 
You then exploit the fact that by definition, $cov(I,X_{pre}) = 0$. This allows you to conclude that if the treated group did indeed have higher/lower outcomes, this can be reduced to their receiving the intervention, because the two groups are randomly sampled from the same population. 
Why doesn't this work in observational data? Because you can't control the selection into treatment and control groups. Consider an intervention, such as receiving counseling when one is unemployed. Not all the unemployed are equal, and selection into the counseling group is bound to have some connection with other attributes.
