As a complement to the other answers, which are very reasonable: your concern about "theory" when using regression where there are no "direct effects" seems to be a concern about causal interpretation, so I'll assume causality is the root issue.
First: you can always apply regression models without any causal interpretation because a regression model is just a model of (at least) the expectation of some conditional distribution, e.g. P(anxiety | depression, memory, attention).
Without a causal interpretation, one interprets a model parameter, say the coefficient on depression, roughly as follows: if we compare a group of people with some value of the depression measure to another group with a measure one unit higher we expect to see that the average anxiety score for that group are $\beta$ higher/lower than in the first.
Here the model is just a summary of the relationships you'd see if you plotted everything as @PeterFlom suggests.
The model itself doesn't change if you start to interpret it causally because the causal assumptions are about counterfactuals that require separate non-statistical assumptions. Although the relationship between statistical model specification and the identification of particular causal effects is a large one (and often conflated, as e.g. in the case of discussions of 'omitted variable bias'), the point here is that a regression model can be considered either as a summary of associations or as an attempt to identify a particular causal effect, as you choose.
Second: Again, roughly speaking, under a causal interpretation regressing anxiety against the other variables is consistent with (though does not uniquely imply) a causal story where those variables cause anxiety (directly or indirectly), no other variables that cause anxiety also have an effect on those variables, and the effect of the other variables on anxiety is the same for all subjects. But you do not have to sign up to this story if you don't want to interpret things causally.
It's also worth pointing out that the other answers here implicitly suggest other perhaps more defensible causal structures, e.g. @January suggests that there are two latent variables of which the four observed variables are only indicators i.e. effects, and that the causal or other relationship of interest holds between the latent variables rather than between the indicators. This leads to a more SEM type of approach and perhaps a more defensible causal story. It also leads to a different model.