It is not true.
I had W-class economy ticket and got the only upgrade last week 29.March as the SEN+ on that specific flight. Flight originiated from FRA. I am very sure, there was also on board passengers with more expensive booking class. Asked the same question also from our local LH office and they confirmed, that the operational upgrades are going always by importance HON->SEN+->SEN->FTL/*G->higher booking class.