Catria, you answered your question in your own post: some faculty think that the General GRE is important and others do not. Admissions committees are composed of physics faculty, so some will think that the General GRE is important, and others will not. In fact, you can replace "General GRE" with almost any aspect of the application (Physics GRE, grades, letters, personal statement, etc) since professors weigh these items differently based on their own experiences. Since you cannot control how individual admissions committee members will weigh these items, the only thing you can do is to create the best possible record that you can, so that all aspects of your application are viewed positively. You can also apply to a range of programs, so that you have a chance of having your weaknesses down-weighted by at least one program (or, conversely, your strengths up-weighted by several programs).
Despite these disparate views, I think most physics faculty would agree that the General GRE is not what will get you in the door (i.e., faculty do not rank applicants primarily based on these scores), but it might keep you out (i.e., a low score on any aspect of the GRE might be sufficient to reject an otherwise reasonable applicant). For reference, the Graduate School (not the department) at my institution expects students in all programs to be above the 50%-ile for all sections of the General GRE. The Graduate School also has a minimum GPA requirement. We can admit students that fall below these cut-offs, but we have to justify why they are acceptable and why we think they will succeed in our program. However, most of our top applicants meet or exceed these requirements, so their precise scores on the General GRE are not usually the determining factor in the admissions decision.