Private pilots can't VFR into the TFR, but they absolutely can if directed by ATC! There's videos on
YouTube from helicopter pilots who radioed in asking for flight following (during the pandemic shut down and reduced airspace volume) and requesting the transit through the TFR, and then getting it. The video is awesome (and rare).
He requests the TFR transit early in the video, and he gets to DLR at about 8:40 in the video.
EDIT: I watched it again, and it reminded me of the first time I watched it, and I got really sad, because we really didn't know when the park would reopen again. Some dark times, there.
EDIT 2: He did it again this time with DCA