ADC frequency response: confused about sinc filter

I can't understand digital filters inside ADC....

Modulators (sigma-delta) works with higher frequencies than the output data rate, so I need low-pass filter before decimation. Ok, it's clear.

Let's say I have a vibration sensor, range DC to 4kHz, frequency response as 2th order low-pass filter with pole at (-3dB) 4kHz, so flat frequency response until cut-off frequency.
I need ODR at 1000SPS, 24 bit, so sigma-delta or SAR ADC, let's suppose 1000 SPS would be available from ADC as ODR decimation factor.

Taking a look to available ADCs I always see sinc as digital filter after modulator (except for LTC2500)....  but sinc filter hasn't flat response (AN-0979, fig.1-2, LTC2500 datasheet, fig.27), so I will not expect flat frequency response from ADC at selected ODR.

AD7766 (AD7766 datasheet, fig. 32, 33, 34) shows flat response, so I suppose it would be overall frequency response including sinc, right?
I am confused about sinc after modulator and flat frequency response I can find on datasheets....

BTW:
LTC2500 sinc filter coefficients are correct? I can see only ones....