Are cards of the same "rarity level" really equally rare in MTG?
I believe that, these days, a card at one level of commonality is pretty much equally common (or rare) as a card at another level.  However, it's pretty hard to work out exactly what the chances of getting a card of a specific rarity is, due to the complications introduced by premium foils, and other maverick card slots such as Innistrad's double-faced cards, which are going to get a slot all of their own.  I dug up the following information from Wikipedia to demonstrate quite how arcane the system of putting together a modern booster pack is:


  15 cards per booster: 1 rare, 3 uncommons and 11 commons; Core Set
  boosters contain a basic land as one of the commons. Starting with the
  Shards of Alara block, booster packs for both Core Sets and Expansions
  began to contain 1 land, 10 commons, 3 uncommons, either 1 rare (7/8
  chance) or 1 mythic rare (1/8 chance), and either a tip card (which
  explains the new rules in the set, such as exalted in the Alara Block
  or Infect in the Scars of Mirrodin Block) or a token (which is of a
  type produced by a card in the set). Also, roughly one in every four
  booster packs contain a foil card, which can be of any rarity,
  including basic land. Since foil cards replace a common, no matter
  what the rarity of the foil, it means that there is a chance that a
  booster pack could contain 2 rares, a rare and a mythic rare, or even
  2 mythic rares. Also, the presence of a foil card means that there is
  a chance that there are two of the same card in the booster pack (one
  foil and one regular), which would not occur otherwise.
  
  Note: Innistrad boosters, first released in September of 2011, contain
  a slightly different proportion of cards due to the introduction of
  double-faced cards. In Innistrad boosters one of the 10 commons is
  replaced by a double-sided card. This double-sided card can be of any
  rarity and either regular or foil, with the likelihood of a specific
  card being present depending on its rarity. Also, there is roughly a
  3/4 chance that the basic land will be replaced by a checklist.
  Finally, non-double-sided foil cards may still be present, probably
  still in roughly 1/4 of the boosters.


I believe this means that in Innistrad, you could get a pack containing
3 Mythics - one in the normal rare slot, one in foil replacing a common,
and one in the double-faced card slot.  And of course, you still hear rumours of errors at the factory producing all-rare packs from time to time!

To answer your more specific question, though, I believe Wizards have print runs of commons, uncommons and rares, in which each card at a specific rarity is printed once per sheet; so in theory at least any given rare (or whatever) should occur exactly as often as any other given rate.  This wasn't always the case: in the old days you had things like "C1" and "C3" rarity, which meant that the first card would be printed only once per "common sheet", making it exactly three times as rare as a "C3", that is to say about as rare as an uncommon! There were also accidents of history, such as when only half of the Legends uncommon sheets were shipped to certain locations (such as the UK, where I lived at the time), making some uncommons easy to get hold of in my location, and some like gold dust...

As I say, I'm pretty sure they don't do this kind of thing any more though.  A rare is a rare is a rare... unless it's a mythic of course!