Blood oxygen level-dependent functional magnetic resonance imaging (fMRI) is a widely used, non-invasive method to assess brain hemodynamics. Resting-state fMRI (rsfMRI) estimates functional connectivity (FC) by measuring correlations between the time courses of different brain regions. However, the reliability of rsfMRI FC is fundamentally compromised by statistical artifacts arising from signal cyclicity, autocorrelation, and preprocessing-induced distortions. We discuss how standard rsfMRI preprocessing -particularly the widely used band-pass filters such as 0.009-0.08 Hz and 0.01-0.10 Hz- introduce biases that increase correlation estimates between independent time series. Additionally, filtering without appropriate downsampling further distorts correlation coefficients, inflating statistical significance and increasing the risk of false positives. Under these conditions, commonly used multiple comparison corrections fail to fully control Type I errors, with up to 50-60 % of detected correlations in white noise signals remaining significant after correction depending on the sampling rate, filter and duration. To mitigate these biases, we recommend adjusting sampling rates to align with the analyzed frequency band and employing surrogate data methods that better account for the statistical properties of rsfMRI signals and reduce autocorrelation-driven false positives. Additionally, we show that structured brain states-such as epilepsy and anesthesia-induced burst suppression-impose low-frequency neural activity that further amplifies these biases, distorting FC estimates. These findings indicate that accepted rsfMRI preprocessing pipelines systematically amplify spurious correlations and call for an improved statistical framework. This framework must explicitly account for autocorrelation, cyclicity, and multiple comparison biases, while excluding or correcting for structured neural activity that further distorts connectivity estimates.