Nope, your friend is absolutely correct. Think of it like this, your wheels are basically gears that are connected to your engine through the axles. When you increase your tire size you do several things.
*raise the cars center of mass
*more kenetic energy gained from bumps
*your tires push BACK on your engine for as much as your engine pushes your tires
It works like this... by increasing your tire size you force your engine to essentially work at a higher gear ratio to move your tires. By updating your gear box like on most heavily modded cars this isn't a problem because more "race designed" gears can compinsate, stock gears however can't always do that. Bigger tires produce more torque when they skid or slip, which causes damage to the tranny. Also because of the larger wheel there is greater angular inertia within the engine. Because larger wheels are often times heavier they have larger rotational kenetic energy, so the engine does the same amount of work as it would for the smaller tires, but much of the work is "wasted" resulting in wear on your engine. Because the center of mass is higher the angular force from any bumps or other things in the road also take more of a toll on your engine than they may if your car was lower. Which is why lowering a car with bigger tires is important, not only for looks.
Hope this answers your question.