Is CIF just an inverted Kaplan-Meier survival curve, and nothing more?
If you're talking about the cumulative incidence function that arises from a Kaplan-Meier estimator, then it's just $1 - S(t)$ where $t$ is time. In R:
library(survival) fit <- survfit(Surv(time, status) ~ x, data = aml) plot(fit) # the standard survival curve plot(fit, fun="event") # the cumulative incidence curve
But, CIF is more commonly used in other contexts, for example in competing risk analysis using cause-specific Cox regression. There, the CIF is not necessarily equal to $1-S(t)$ because it takes into account the competing risk, estimating the risk of an event happening given survival up to time $t$ and also that a competing risk hasn't occurred up to time $t$.