I tested my Sony ICF-P26 after reading about your poor experience with it earlier on. Mine works great. The selectivity, understandably, is wide for a DX radio but it still will DX. I think it's using the standard Sony CXA1019 / ceramic filter configuration used in their ICF-38 and other radios, although the ICF-38 has a noticeably narrower bandwidth than the P26 (possibly a different ceramic filter, or maybe higher Q in the loopstick or other circuitry somewhere). That said, if you want to DX with the P26 than hold it further away from a loop antenna than you normally would with other radios. This will enhance selectivity. You can do the same with Walkmen radios and get good results the same way.
Two nights ago I received KGB-AM (the former KFMB) San Diego on 760 khz, on my ICF-P26. In my location, there is a strong local on 770 and a strong regional on 750 khz, so KFMB / KGB is difficult to hear normally. On most radios there is a lot of splash from the two adjacents. On the P26, without the loop, the splash covered 760. With the loop, and the P26 placed away from the loop, I could hear KGB-AM clearly, with some splash. I had to keep the P26 six inches or more away from my Select-A-Tenna to hear KGB-AM. Any closer the radio's ceramic filter was swamped by 770 and/or 750.
Unaided I can hear most of the regionals and some DX stations with the P26. The CXA1019 IF chip has a full RF amp built in. The P26 radio's main deficiency is probably the short loopstick. Otherwise, it's a capable radio for most listening and some DX uses. I would think it's good on batteries, too -- which would be of use in disasters and emergencies. Sounds pretty good through the headphones (momo, of course, although the jack is stereo).
Key point: If you really want to DX with it, use headphones, and manipulate the loop / radio, keeping the radio six inches or so from the loop when you need the selectivity.
