i know exactly what you're talking about, i drive my dads 2000 528i a bit and when i drive it, well, exuberantly
it smells of burning oil and smokes a bit. you're educated guess is exactly right, these engines are known to leak a little oil when they're being pushed a little and it just burns off the hot engine, causing the smell and smoke. As for our 528i my dad looked at it, found nothing wrong, and we took it to a mechanic for a second opinion and he confirmed everything. it leaked a bit of oil, nothing sever though, but aside from that the engine was fine
im not saying there isn't anything wrong with your car but it is a common issue and might be nothing at all. hope this is of some help