If you happen to be nearby a broadcast station of any significance, those diodes may hurt more than they help.
In fact, though it is unlikely, it is not impossible that you may be re-radiating harmonics or intermodulation from those nearby radio stations.
My advice is to use this with relatively short antennas or to keep signals attenuated as much as possible.
A better idea would be to put those diodes behind a selection of passband filters. This would help eliminate problems with nearby broadcast stations and provide your receiver with additional immunity from strong nearby broadcast stations.
Although theoretically it's possible (as you and others have said) most other Sangeans (including their flagship radio the ATS909X) have protection diodes. And they are in some Sony radios as well.
If he's close enough to an AM broadcast station, he could get intermod just from being close enough to the station, diodes or no. The DX-390 is a great receiver but it is a bit hot and it's a fact that it can overload on strong signals.
Mine did it before diode protection and after diode protection was added -- on SW, on some occasions (20 meter CW showing up about 455 khz or 1 mhz below the band, strong local RTTY showing up in one of the SW bands from time to time, etc.).
In my case, the diodes made no difference in intermod/overload. But at least I don't have to worry about my radio's RF amp getting blown by static electricity.
The shorter antenna idea you suggested is a good one. Unless he's in a very low signals area, even a 20-30 ft antenna will work very well. I used a 100 ft antenna for a while and got good results, but I"m in a hole, in a low signals area. When I took my DX-390 to Louisiana a few years ago even 15-20 ft of wire plugged into the external antenna jack overloaded it. It worked just as well off the whip. Right now I use a 20-25 ft indoor antenna and get good results.