  According to Bekenstein's area law, the black hole entropy is identified
holographically -- with one quarter of the horizon area. However, it is
commonly believed that such a law is only valid in Einstein's theory and that
higher curvature corrections generically give rise to its modifications. This
is for example the case of black holes in Lovelock gravities, or their
four-dimensional cousins in the recently discovered 4D scalar-tensor
Gauss--Bonnet gravity where one naively `finds' (classical) logarithmic
corrections to the Bekenstein's law. In this Letter we argue that such
logarithmic corrections originate from ignoring the shift symmetry of the 4D
Gauss--Bonnet gravity. When this symmetry is properly taken into account, there
is no longer any departure from the area law in this theory. Moreover, the
first law remains valid upon modifying the black hole temperature, which can be
derived via the Euclidean grand canonical ensemble (Brown--York) procedure, but
is no longer given by the surface gravity. Interestingly, we show that upon
similar modification of the black hole temperature the area law can also
prevail for black holes in higher-dimensional Lovelock gravities.
