Condition usage clarification

I think that the meaning of this sentence is stupidly verbatim: the author simply notes the (almost obvious) fact that this construct allows sharing the localized by Module variables between the Condition and the rhs (which resides inside of the Module). In contrast, if we move the Condition outside of the Module, we won't have the localized variables shared between the rhs and the Condition:

f[x_] := Module[{u}, u] /; EvenQ[u]

f[2]

f[2]

Probably this shouldn't be in the Details section: this statement is too obvious to reside there, it doesn't add something meaningful. But from the other side, there are some non-obvious under-documented "smart" rules on how different scoping constricts interact with each other: may be the author simply stresses that this obvious behavior is by design and we may trust it without risk...

I never understood what that line in the documentation meant until I saw use of it in answers on Stack Overflow, i.e. Partial evaluation in Mathematica. As such I am in the camp that feels this documentation could be written more explicitly for a user who is not already familiar with its use.

I propose something along these lines:

For With, Block, and Module there exists a special construct lhs := With[{vars}, body /; test]. In this specific instance the Condition applies to the entire definition upon lhs as if it were lhs := rhs /; test but in which test may depend on the localization and evaluation of vars. This construct applies also to RuleDelayed, UpSetDelayed, and TagSetDelayed (short forms :>, ^:= and /: :=).

The scoping construct must constitute the entire right hand side of the assignment or rule, and the Condition must constitute the entire body of the scoping construct, less any additional Condition applied to each.