The 3k mile recommendation comes from these two Valvoline guys, in this Motor Oil Geek video. They note that the filter is pretty dirty after only 3k miles, so they recommend running the oil and filter for only 3k miles.
But wouldn't it seem, that by the third R&P oil change, that it could be ran longer?
I went back and watched the video again, and could not find where they talked about a 3k oil change. But starting at about 14:30, they talk about potentially overwhelming the filter. It may have been here on BITOG, in discussing this video, that others suggested that perhaps a 3k oci was wise with R&P.
But perhaps just a filter change at about 3k - 4k miles, may be the thing to do.