Newton's laws of motion would like to have a talk with you about those statements. A heavier vehicle absolutely needs more energy than a lighter one when all other factors stay the same.
Which comes to Newton's laws of motion, the two concepts of inertia and Newton's second law: "F=ma", come into play. If the course is a straight 100 mile segment with no elevation gain - then the dominant fuel expenditure will be counter-acting aerodynamic drag. When trains haul many cars, the train cars are drafting behind one another, meaning those cars do not need any force to overcome drag, just the lead car needs to do that.
So, places where trains do badly, will be places where weight matters. Urban environments when stopping/starting a lot - trains will keep it slow. Very hilly/mountainous courses - trains "nope" that and require shallow grades. Which goes to show, if you're spending most of your time fighting gravity - then weight is really important, if most of the time is fighting aerodynamic drag, then weight becomes less important as aerodynamic drag decreases. For example, it does not matter as much how heavy a bullet train is, the drag coefficient is a better indicator of overall fuel cost rather than carry weight.
I hate when people make smart-ass claims with surface level knowledge at best.
Yes, actually. The most common example of this is drivetrain power loss, which EVs are not immune to. Tesla engineers have stated that they are ~15% which is about the same as with ICE vehicles.