On its own, though, that reading won't quite work, either. Some subjects are just obvious. The Sun is hot. Water is wet. 2+2=4. And so on. I don't need to consider opposing views -- the Sun is cold, water is only wettish, 2+2=5 -- in order to believe that these are true. The reasons I don't need to consider opposing views are not all the same. That the Sun is hot I know because I know the surface temperature, in at least an approximate sense, and I know it vastly exceeds what I could tolerate. I call temperatures I have a hard time tolerating "hot", so the Sun is very certainly hot. I consider water to be wet because all instances of water I have encountered produce in me the experience which I associate with wetness. 2+2=4 because that is a definitional truth of arithmetic, which can be grounded in various more fundamental mathematical views. Or, in summary, I know these by inference from other beliefs, by inference from prior experience, or by inference from rules of a system. To really simplify even further, if the issue is one which can be settled by inferences from what I've already got at hand, then it seems I don't need to consider opposing views before settling on an opinion and calling it true.
Of course, I could always be wrong. This is not an infalliblist doctrine, by any means. The question is at what point my obligation to only believe things I have good reason to believe is discharged, and it seems that it usually gets discharged when I can make good inferences from what I already know.
This method won't settle all issues. Sometimes, I'm exposed to things I know nothing about, or sufficiently little about that I cannot make any good inferences from what I already know. Sometimes I exceed my past experience and experience something novel. I had no idea what bulgar would taste like until I tried it (answer: kind of like a combination of wheat and sesame seeds). I know nothing about neurophysiology, and claims about how brains operate tend to confuse me on that basis. And so on.
So, when the "good inferences" method fails, am I then obligated to consider all possibilities before making a considered judgement? The answer, simply, is "no". The reason the answer is "no" is that my epistemic obligation discharges when I can make a good inference from what I already know. The failure to pass that hurdle is what sends me off with another method -- I have insufficient information already at hand to support a good inference, so I try to get more information. Once I pass the threshold, though, once I gain enough information to leap over the hurdle of being able to make a good inference, then my usual strategy can kick in again and my obligation can be discharged.
The objection that could be raised here is that I'm justifying dogma and closed-mindedness. I'm doing no such thing: what I'm suggesting is that I only have good reason to ensure that everything I believe is supported by good inferences. When my inferences are challenged, either by attacking the chain of reasoning or by attacking the beliefs on which the reasoning is founded, then I no longer can claim to believe things based on good reasoning. I would then have two options: show that the attack fails (that is, that my reasoning actually is good or its founding beliefs well-grounded), or redeploy my reasoning (and thus potentially refine my beliefs, possibly radically).
The claim is not that, once one has passed the obligation of good inferences, then one never has to think again -- if I were saying that, then the charge of dogmatism and closed-mindedness would be apt. Instead, the claim is that there is a threshold beliefs must pass in order to be taken seriously: they must be founded on good inferences from past information. Once their passing that threshold is called into question, then the obligation cannot be said to be fulfilled, and one is therefore obligated to re-found one's beliefs on good inferences.
That, I think, is really the best sense that can be made of the "two sides" claim: that one shouldn't believe things dogmatically or instinctively, but because one has good reasons for them. However, in many cases, this doesn't require one do anything more than inspect what one already believes. Which is why it is important to engage in open and fair debate with different-minded people, for only through that mechanism will one be able to ensure that one's inferences are genuinely good.