Short answer: Admissions is similar but not quite the same at each graduate institution and thus you should follow the guidelines as outlined by each school and department you are applying to. Dates and requirements may vary, but not by much. Yes, you are correct - the general practice in U.S. schools is that if a certain aspect of your application is weak, the strong components have the capacity to "offset" the weak areas. However, this is highly contingent upon whether the graduate school requires a minimum GPA and/or GRE score, as well as what parts of the application matter most to the program you are applying for.

Elaborating on the short answer: Most U.S. undergraduate and graduate programs take on at least somewhat of a holistic approach, i.e. a focus on the overall prospective candidate, whereby one's application is considered for its overall content. For example, if your statement of purpose is very strong, it could offset a less-than-stellar GRE score. Within the U.S., it is often the case that your admissions application (as well as conditions for timely progress in your program after being admitted) have two different sets of requirements that must be followed: that of the graduate school and that of your prospective department. Therefore, when applying to schools, it is important to read up on both the graduate school and the department. The general graduate admissions application requirements might differ from your department's requirements in minute ways. For example, your application might not ask for a writing sample, but the department website states an expectation for a writing sample to be sent to the graduate coordinator's email.

Keeping in mind that each school (and program within the school) might consider applications differently because it is typically based on admission/approval from both the graduate school and the department you are applying for, many institutions not only state the application components but moreover will tell you the extent to which certain factors are weighted. Some graduate schools emphasize that they would prefer students with a GRE score of x or higher, typically with an asterisk that states that the GRE is one factor of many and students are still encouraged to apply even if they do not meet the desired score. This information is generally listed in the admissions FAQ section of the graduate school and/or department website(s). If the information is not provided, you can contact the department's graduate coordinator and/or prospective adviser on the matter.

Within the social sciences, the statement of purpose and letters of recommendation are arguably the most important components. If the program is writing intensive, it is likely that the verbal reasoning and analytical writing portions of the GRE might matter significantly more than the quantitative reasoning section. (I have also been told that some programs do not require GRE scores, but it seems this is mostly the case for Master's programs rather than Ph.D.'s.)

Again, the extent to which each component of your application matters will vary greatly amongst schools and programs, but the general rule to follow is that if your undergraduate grades/transcripts are not very good, you should excel in the other parts of your application and communicate relevant strengths to your recommenders so that they know to highlight these more positive aspects within their letters of recommendation.

On another note, thankfully many Ph.D. applications in the U.S. now reserve a section for you to explain any "blemish" on your record; this could be anything from explaining a bad grade to elaborating on a particular skill that the application did not allow you to do. Think carefully about how you would like to word the weaker parts of your application, but this section is indeed reviewed and considered. If your application does not have a place to state this, I have found that emailing the graduate coordinator works just the same, for they might be able to add a note to your file for you (just make sure to ask nicely!). Lastly, communication with prospective advisers (if applicable) is key; not only can they (potentially) vouch for your strength as a prospective candidate in ways that an application cannot, but getting to know you ahead of time could also assist them if they are from an institution whereby advisers can nominate their incoming students for awards, funding, etc.