It is true, but not at all.
What do I mean with that? First, let's remove your documentation question. The following paragraph is §3.13 of the PowerShell version 3.0 language specification :
, , . , -, . . , , , .
, .
, .
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PowerShell - , :
, BeginProcessing() . "" - - , .
, , .
!
begin, process end, , .
5 , , Write-Host, , (. ):
PS C:\> 1..5 |first |second |third |Out-Null

, PowerShell -OutBuffer, :

, !
, .
Write-Host , , , , .
function Test-Pipeline {
param(
[Parameter(ValueFromPipeline)]
[psobject[]]$InputObject
)
begin {
$WHSplat = @{
ForegroundColor = switch($MyInvocation.InvocationName){
'first' {
'Green'
}
'second' {
'Yellow'
}
'third' {
'Red'
}
}
}
Write-Host "Begin $($MyInvocation.InvocationName)" @WHSplat
$ObjectCount = 0
}
process {
foreach($Object in $InputObject) {
$ObjectCount += 1
Write-Host "Processing object #$($ObjectCount) in $($MyInvocation.InvocationName)" @WHSplat
Write-Output $Object
}
}
end {
Write-Host "End $($MyInvocation.InvocationName)" @WHSplat
}
}
Set-Alias -Name first -Value Test-Pipeline
Set-Alias -Name second -Value Test-Pipeline
Set-Alias -Name third -Value Test-Pipeline