Fast,
I have 5000hrs on type as a commander,I can tell you that your friend is not only wrong,he is dangerous as well!
Engine failure 'just' after take off has alot to think about.You must 1st secure the engine so it wont give you further problem.Fly a proper departure,be it a SID,EOSID,vectors,proceed to holding waypoint etc.Then take time to analyse the engine.Don't forget you can be as much as 8tons(-400) over your max landing weight! Why rush to come back for a single engine landing if you could have normal 2 engines landing if you can get the other engine to start? (go have a good look at the engine out flap 15 landing distance/speed at max takeoff weight). Engine fuel leak has a limited rate.If a tank went zero just after take off with engine out due fuel exhaustion,it may well be a tank leak rather than an engine fuel leak,there isn't a checklist for tank leak.(happened to me once on a long flight over water).As long as you have enough fuel to come back,the rest of the fuel leak away can reduce the a/c landing weight/speed.Also,since the engine fuel leak has a limited rate,it is always important to analyse carefully,don't jump the gun.