Have you looked at the datasheet for one of the SiLabs chips in many of the modern popular DX and SW radios? According to their datasheet blurb, "the integrated LNA and AGC optimize sensitivity and rejection of strong interferers allowing better reception of weak stations." Isn't that similar to what a tuned RF section does: amplify and tune the antenna circuit ahead of the IF section? There's a block diagram in the datasheet, although it's not super detailed.
Here's a datasheet for the chip I believe is in the newer Sangean PR-D5's:
http://www.silabs.com/documents/public/data-sheets/Si4730-31-D50.pdf
Of course, with DSP, you probably don't have the standard superhet design after the RF section. According to the datasheet I'm looking at, the next stage after the RF section is the Analog to Digital converter. As I said before, I'm not a tech, so a lot of the info on the datasheet is probably above my pay grade.
But it looks similar to a TRF to me, in concept -- at least the way they describe it (I wish they described it better). It doesn't sound like it's a dumb RF amp section, like most modern analog IF chips have (including the chip in the SRF-59). The block diagram shows a tuner symbol in front of the RF amp. Then again, maybe it's a 'dumb RF amp' like the one you described was in the GE tube radio.
Although I'll admit, a lot of those 'dumb' RF amp sections in those analog IF chips do quite well. My Sony ICF-38, which has one of those chips, almost performs as well as a Superadio II, even though it has a 60mm loopstick inside it.