wrstdude thinking toe-may-toe and I'm thinking toe-mah-toe:
Absolutely they were achieved on purpose. Two strong running games already existed before two limited QBs took over the reigns of their respective offenses. Gore and Lynch is where both teams made their money offensively. Also, I'm not sure where you're coming up w/ their offenses being pitiful as both were top 10 (SEA 8 SF 10).
Of course a top 5 defense will help. Not sure I said otherwise or that even they were successful ONLY because of their offense. Not many teams that have sustained playoff success are deficient in an area.
My point, which has evaded you, is that a strong running game w/ limited passing can, in fact, still score points in the NFL which is part of the recipe of winning.
I'm not sure you understood my point or I just didn't make myself clear enough. Then in your next sentence you made my point or at least part of my point. I'm pretty sure they'd rather average 400 yards passing and 400 yards rushing.

But lacking the right personnel to accomplish that formidable task ("two limited QBs") they designed an offense that would best utilize what assets they
did have on offense. I think we both probably agree with what I just said.
Now, did either of those two teams want/prefer to have limited QBs who were/are incapable of regularly producing 400 yards in passing offense per game? I think not. Did either of those two teams want an offense that would struggle mightily to overcome big deficits with only a top notch running game? Again, I think not.
When you say this "you'd have a tough time convincing most people that they haven't been successful." you need to make it clear that you're just talking about their offense because I took what you said to mean that you were talking about the teams being successful in general terms. Knowing now how I took your words, you can understand why I talked about their defenses. More on the effect of the defense on the offense later.
If you were limiting it to just their offenses being successful then I'd have to totally disagree with you and in the strongest possible terms. A team which only has a strong running game and a mediocre to crappy passing game (173 YPG passing), has to rely on frequently having good field position to be successful and even then it's a limited success IMO. How is that accomplished? Again I'll bring in the "A Great Defense is the Key to Success When You Only Have a Great running Game in the NFL" part of my argument.

It only takes one or two runs being stuffed to stop a running game and when you start off in bad field position that's more likely to happen.
In addition, continually starting in good field position makes every offense look much better because their whole playbook is available and the offense can take more chances. I don't care where the Shehags or Whiners offense is in the statistical standings, neither of them have a top offense. You only have to look at teams like the Shegals, Patsies, Packers et cetera to see what a top offense looks like. IMO. Plus, I wasn't talking about the Hags or the Whiners when I referred to pitiful offenses because they are blessed with great Ds that make their offense look better. I was talking in general terms. Sorry for not making that clear.
Last but not least, your point didn't evade me at all. Even the way you worded it makes my point. You could have said "a strong running game w/ limited passing will, in fact, still score points in the NFL" but you said "a strong running game w/ limited passing
can, in fact, still score points in the NFL." That slight change shows me that you realize how hard it is for a team to succeed with only a good running game. But yes, it
CAN be successful. Is is sometimes necessary to have one? Yes. Do I purposely want to try to have a team that has to live or die with this motto "a strong running game w/ limited passing can, in fact, still score points" by hiring an OC who specializes in that? My answer is no way Jose.
That's all just my opinion of course but it's based on, wait for it...math.

Your odds of having success are much greater with a balanced attack. Even Martz thinks that. Now.

With the changes in the rules the pendulum has swung to the passing game being of paramount importance IMO.