Inconsistent conclusions are obtained from recent active galactic nuclei (AGNs) accretion disk inter-band time-lag measurements. While some works show that the measured time lags are significantly larger (by a factor of $sim 3$) than the theoretical predictions of the Shakura & Sunyaev disk (SSD) model, others find that the time-lag measurements are consistent with (or only slightly larger than) that of the SSD model. These conflicting observational results might be symptoms of our poor understanding of AGN accretion physics. Here we show that sources with larger-than-expected time lags tend to be less-luminous AGNs. Such a dependence is unexpected if the inter-band time lags are attributed to the light-travel-time delay of the illuminating variable X-ray photons to the static SSD. If, instead, the measured inter-band lags are related not only to the static SSD but also to the outer broad emission-line regions (BLRs; e.g., the blended broad emission lines and/or diffuse continua), our result indicates that the contribution of the non-disk BLR to the observed UV/optical continuum decreases with increasing luminosity ($L$), i.e., an anti-correlation resembling the well-known Baldwin effect. Alternatively, we argue that the observed dependence might be a result of coherent disk thermal fluctuations as the relevant thermal timescale, $tau_{mathrm{TH}}propto L^{0.5}$. With future accurate measurements of inter-band time lags, the above two scenarios can be distinguished by inspecting the dependence of inter-band time lags upon either the BLR components in the variable spectra or the timescales.
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