A few 'reasonable' explanations are enough, and they are not (much) interested in making the science advance.
I too need to read that article, but I will go ahead and state my view of this issue:
As to the first part of the sentence, yes one or a few "reasonable" explanations are sufficient to satisfy our most pressing need, which is to banish the allegations of the religionists that the Sun was divine, or part of a divine order.
But as to the second part of the sentence, when I see that sentiment stated in that way (and we see it often) I think that the wording is too negative and arises from modern prejudices against Epicurus. I see Epicurus as being strictly logical in his approach, which is that once he has determined (through science!) that the end of life is happiness/pleasure, then he is logically consistent and holds the tests of ALL actions in life, including the study of science, to the test: "Does it advance our happiness?" Once you conclude that there are no criteria given us in life by nature other than pleasure and pain, then you apply that conclusion rigorously and without exception.
The negative presumption that is conveyed in "not much interested in making the science advance" is the anti-Epicurean conception that there are ends in Nature which are justified IN THEMSELVES apart from whether they bring pleasure or avoid pain. Such a conclusion is logically ruled out by Epicurean philosophy.
On the other hand, Epicurean philosophy also asserts that since there is only one reason to do anything in life (pleasure/pain) you are going to do everything in life that is practical for you to pursue pleasure. And MOST CERTAINLY the advancement of science is a tremendously useful tool for advancing pleasure and avoiding pain, so MOST CERTAINLY an Epicurean is going to appreciate and pursue the advancement of science as a tool for better living.
So in my view the many times that we see statements like "Epicurus wasn't much interested in science" we are really seeing the complaint that "Epicurus wasn't interested in XXXX for the sake of XXXX itself." That argument makes no sense without realizing that the impetus behind it is the assertion that Epicurus was wrong and that he should have valued "XXXX in itself" (most generally, they are asserting "virtue" or "piety" as goals in themselves).
Therefore I think we ought not be afraid of or concerned about that "Epicurus didn't value science" argument, and instead turn the issue around and use it as a teaching opportunity for explaining why Epicurus taught what he taught.
End of rant!