I am saying there are inaccuracies.
dB is a function of power ratio: 10 * log (P2/P1). Thus when P2 is half of P1, we have 10 * log (0.5) = -3 deciBels. Amplitude normally refers to voltage, whose square is proportional to power. At the 3 dB point in your low pass filter example, amplitude is reduced to 0.707 (square root of 0.5) of its full value.
A first order filter has an asymptotic slope of 6 dB/octave, not 3. The response of the filter is -3dB at the "corner" frequency - the point where the 6 dB/octave asymptote meets the full-amplitude line. Higher order filters have an asymptotic slope of 6n dB/octave, where n is the order of the filter.