Not sure that I would - it would depend on a lot of factors, including how much money I made, but the University of Alabama is an excellent school that lots of people go to graduate school from.
Neither is Claremont McKenna or Pitzer, Davidson, College of the Holy Cross, Rhodes College or Agnes Scott, Hamilton, Washington and Lee, Colgate, Colby, or a whole host of other really excellent, top-ranked liberal arts colleges. (Who knows - they might be in the 50-100 range, but we don’t know.) Neither are a bunch of other well-regarded public universities like UMass-Amherst, UConn, the University of Georgia, University of Pittsburgh, Miami U, Clemson, Florida State, etc.
Both lists are skewed by size. Table 4 favors really small schools because proportions are much more largely affected by small changes at liberal arts colleges with smaller graduating classes than at large universities. Notice that Table 4 is dominated by small colleges, and even the research universities that have ended up on there tend to be smaller research universities - the few public schools that ended up there are small specialized schools like NMIMT or Colorado School of Mines, or smaller sized schools like William & Mary. The only really large research university on there is Berkeley.
And on the flip side, Table 2 obviously favors larger universities - because they’re based on pure numbers. If you graduate 10,000 students a year, even if only 10% of them go to graduate school that’s still way larger than a college that graduates 500 students a year and sends half of them to graduate school. That’s why there are no small liberal arts colleges on that list - none of them even graduate 734 students a year (the smallest number on the list). But that doesn’t mean it’s better to go to Rutgers than Columbia (further down) or Pitt (not on the list at all).
There are two important takeaways for me:
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This is the list of the top 50 - by proportion and by raw numbers - but that’s out of 3,000 colleges in the U.S., which makes it the top 1.7%. A school’s absence from the lists means nothing. (Quite frankly a school’s presence on the top list could be a function of sheer size, although all of the schools on both lists are quite good.)
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The ecological fallacy is assuming that averages apply to individual situations. I refer back to the points I made in the first post. The students who go to Stanford or UT-Austin or Reed are wealthier and more ambitious on average than the students who go to Georgia Southern or the University of Alabama or Cal State Northridge. Sure, I’m willing to bet that the encouragement, atmosphere, opportunities and rigor are such at Reed, Swarthmore, and Carleton (and Wisconsin and Michigan and Stanford) that students are better-prepared for graduate school and exposed to more careers and ideas that would necessitate or highly recommend graduate school. But they’re also simply more likely to have intended to go to graduate school in the first place, or have role models or influences in their lives to encourage them to go to graduate school independent of what college they chose. And if those same students had chosen to go to the University of Alabama or Georgia Southern or Southern Methodist or Cal State Northridge instead - they probably still would’ve gotten into graduate school.
I’m not saying don’t use the tables; I’m saying weigh the tables appropriately with other information.
As an only somewhat-related aside, one of my favorite things that NSF does is examine origins of black or African American S&E doctorates. Fully 24% of black students with PhDs went to an HBCU for undergrad, despite the fact that only about 8% of black college students go to an HBCU. Spelman, my undergrad, is ranked #2 as a producer of S&E doctoral degree recipients from 2002-2011 despite being a small LAC with only 2300 students. Some of that is size and distribution of black students but not really - University of Maryland College Park (which is 13% black) has more black students at it at any given time than Spelman’s entire student population. AND what makes it even more awesome is that this is in science and engineering fields and Spelman is a women’s college. 
Still, I don’t think it would make me send my son or daughter to Tougaloo or Southern over Harvard or UMD.