I don't really agree. Of course doing all the 'core duties' of applying to residency is your responsibility, but some schools (and particularly MD schools) do a far superior job of advising applicants on where to apply, guiding them through the process, hooking interested students up with specialty mentors, etc. You have this attitude mostly because you (like me) went through the process on the DO side - a place in which advising is often nonexistent and you generally have to figure everything out yourself, with plenty of guesswork along the way. But as DOs, our schools really should be doing a lot more for us than they are - that's what the MDs get, after all.
Also, if you attend an institution in which department chairs and/or program directors in your specialty are well-connected and helpful to students in terms of making phone calls, writing letters etc, this can be very helpful to your cause. You can sometimes make up for this by 'grabbing life by the horns' as you suggested and meeting influential people on aways who can do this for you, but that's just so much additional legwork that you might not have had to do otherwise.