This is only true if the other airline gives access to the non-Skyteam lounge. Otherwise the airline you flew one may have been confused and thought since you were ElitePlus that they should give you access. Basically DL only provides the benefit to it's eliteplus members for Skyteam lounges. What the other airline provides based on your class of service/elite level is up to them. However unless that airline is willing to provide you access you can't show up to the lounge unless it's a Skyteam partner lounge and get access.