MacBook Pro does 3 beeps at startup once in a while, AHT finds nothing

My brother's early 2011 MacBook Pro intermittently refuses to boot: instead of doing the normal boot chime and the grey screen, it produces three short beeps every five seconds without the screen turning on at all, until the power button is held long enough to shut it down. This is consistent with the symptoms of failing RAM.

Also, at least on two occasions, the computer had a kernel panic and failed to reboot with the symptoms described above. The two panic logs point to kernel memory corruption:

*** Panic Report ***

panic(cpu 0 caller 0xffffff8027d7a52d): "a freed zone element has been modified in zone kalloc.8192: expected 0xc0ffe143edc4efc but found 0xc0ffee143edc4ef8, bits changed 0x4, at offset 8184 of 8192 in element 0xffffff803efa4000, cookies 0x3f00119400778efc 0x53521669530c441"@/SourceCache/xnu/xnu-2782.1.97/osfmk/kern/zalloc.c:496

and:

*** Panic Report ***

panic(cpu 0 caller 0xffffff8027805990): "Possible memory corruption: pmap_pv_remove(0xffffff80339494e0, 0x7fff79'91000, 0x118bb, 0x80000000118bb024, 0xfffffff80c092bb34, 0xfffffe94b95cec88): pv not on hash, head: 0xffffff80339493a8, 0x7ff79d91000"@/SourceCache/xnu/xnu-2782.1.97/osfmk/i386/pmap_internal.h:841

However, the Apple Hardware Test software, downloaded from Apple by starting the Mac with ⌥D, fails to find any issue, even with extended tests on. My brother dropped his Mac at the AppleStore, they kept it for 48 hours, and were not able to reproduce the problem. The OS was also reinstalled from scratch at some point.

I've seen it happen myself, but short of recording it and showing it to the Apple guys as a proof that something's wrong, I'm not sure what to do. Are there any further troubleshooting step that I could take?

As far as I know, the RAM is original. I don't have replacement RAM available myself to try.