This is a complicated issue.
Statistically speaking, schools with higher LSAT admission requirements tend to have higher bar pass rates. So, in the aggregate, higher LSAT admission criteria tend to correlate with higher bar pass rates at the law school level.
However, when analyzing on the individual level the correlation between LSAT score and passing a bar exam on the first try, the LSAT score alone is a rather weak predictor. If all we know at all about an applicant sitting for a bar exam is the individual's LSAT score (in other words, we don't know the school he/she went to, or the grades he/she received in law school, or any other factor at all about the individual), the LSAT score alone is a weak predictor of success on the individual's ability to pass the bar exam on the first try.
Another difficulty arises by the question presented by this post. The question relies on the metaphorical use of the word "reflection." I suppose bar passage rates "reflect" both admissions criteria of certain classes and "quality" of instruction. However, you cannot say with much statistical confidence that an individual with a 160 LSAT has, say, an 85 percent chance of passing the bar on the first attempt.
As far as the measure of the quality of instruction, there is one argument that no law school really prepares you for what many consider to be the hardest part of most state bar exams: the multi-state bar exam ("MBE"). The MBE is a 6 hour, 200 question multiple choice exam. The MBE tests on "majority rules" in many cases. In other words, what most states do across the country. It also tests on common-law crimes. Because, most, if not all, states have enacted criminal codes, the criminal law is largely statutory. Most criminal law professors "teach" the statutes from the codes. In other words, they "teach" the real law of the jursidiction. Although many law school professors will allude to the majority rule, or the minority rule, or in the criminal law example, the old common law rules, in their lectures, most law schools emphasize the law of the jurisdiction where they are located. What's more, most first-year law school exams are presented in an "issue spotter" essay exam format. This last statement is, of course, a generalization. But historically, multiple choice was rarely used on a law school exam. So, in this sense, law school does not "prepare" you to take what many consider the most important part of the bar exam--the MBE. And in some jurisdictions, if you don't score at the least the minimum MBE score they want for that jurisdiction, they don't even grade the essays and you fail.
With all this said, I still feel that law school does prepare you for the overall bar exam preparation necessary for a state bar exam (hint: take Bar-bri when studying for the bar exam). In other words, you master the language of the law and the key concepts in law school. Then, when you study for the bar exam, you can move through the massive amount of material fast enough to cover most of it before the exam. For the MBE, you end up having to learn what many refer to as "MBE law"--which isn't always the "real" law of the jursidiction where you are sitting for the bar. But you must know these rules to pass the MBE.
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