How to propagate -Verbose to module functions?

According to answers like this one and my own experience, Powershell can take care of propagating -Verbose (and -Debug) automatically, which is very convenient. However this stops working when the functions which I want to propagate verbosity to are in a module. Code used for testing this:

Create a directory called Mod somewhere, suppose in c:, and add 2 files:

File c:\Mod\Functions.ps1:

function Show-VerbosityB { [cmdletbinding()]Param()
  Write-Output "Show-VerbosityB called"
  Write-Verbose "Show-VerbosityB is Verbose"
}

File c:\Mod\Mod.psd1:

@{
ModuleVersion = '1.0.0.0'
NestedModules = @('Functions.ps1')
FunctionsToExport = @('*-*')
}

Now crate the main script, say c:\Foo.ps1:

Import-Module c:\Mod

function Show-VerbosityA { [cmdletbinding()]Param()
  Write-Output "Show-VerbosityA called"
  Write-Verbose "Show-VerbosityA is Verbose"
}

function Show-Verbosity { [cmdletbinding()]Param()
  Write-Output "Show-Verbosity called"
  Write-Verbose "Show-Verbosity is Verbose"
  Write-Output "Testing propagation"
  Show-VerbosityA
  Show-VerbosityB
}

Show-Verbosity -Verbose

Results in

PS> . C:\Foo.ps1
Show-Verbosity called
VERBOSE: Show-Verbosity is Verbose
Testing propagation
Show-VerbosityA called
VERBOSE: Show-VerbosityA is Verbose
Show-VerbosityB called

Why is the Write-Verbose in the module's function skipped, why does propagation not behave like it does for Show-VerbosityA? (If I just dot-source Functions.ps1 instead of importing the module, the line VERBOSE: Show-VerbosityB is Verbose is printed). I could make propagation manual by e.g. calling Show-VerbosityB -Verbose:$PSBoundParameters['Verbose']. Or are there other, preferrably shorter, ways? It is quite messy if functions behave differently depending on whether they are part of a module or dot-sourced.