Does a matched filter really improve SNR?
There is no contradiction. Matched filters are often used because they are an implementation of a sliding correlator, which is the optimum detector (in the maximum-likelihood sense) for linear modulation in the AWGN channel. That is, the SNR at the output of the matched filter will be maximized when the filter lines up with the point of reception of the signal that the filter matches.

This doesn't contradict the known properties of your receiver (i.e. its noise figure). The point to notice is that the SNR can be different at the input of the matched filter than it is at the filter output. The SNR at the matched filter input (i.e. your front end's output) is determined by the signal power at the receiver input and the noise figure of the front end. But by applying signal processing techniques, like matched filtering, you can improve that SNR to achieve more accurate detection.