The report comes from Colin Moriarty on his 153rd episode of the Sacred Symbols podcast at the 02:03:37 mark.
Moriarty notes that he was told the overload of post-apocalyptic games in the first-party — Killzone Shadow Fall, Horizon Zero Dawn, Days Gone, and The Last of Us were all being developed or in pre-production at the time — was an issue that PlayStation was 'cognisant' of during the PS3 era.
The three mainline Resistance games in the series had done well (ignore Burning Skies, please) and so another in the series was pitched by Insomniac.
Remember, this was before Sony had bought the developer, so the studio held a little less clout over what projects it could make:
"Resistance 4 was pitched to [PlayStation] and [...] they declined Resistance 4 because it sounded too similar to The Last of Us and they didn't want the two games overlapping with each other. So, Resistance was shut down at that point."
Moriarty is a reliable source with friends who worked at the studio and rarely speaks about the deep bowels of the industry unless he is saying something with absolute certainty.
Sony apparently halted the development of a fourth game in Insomniac's staple PS3 series, Resistance.