And I've noticed that, too...cool!

Brian, that is something that Natasha Shneider taught me years ago, and I regularly use with singers.

Today I had a guy in the studio with a nice-sounding voice for the material (emo/rock). He gets halfway throught the first verse OK and the second half slowly goes up an entire half-step. 4 takes later, trying everything (headphones, no headphones, head up/back/ whatever- always the eventual creep up a half step above the tonic. Finally I asked "Is this the melody?" and sang it for him. Indeed it was, so I recording it, played it back, and he sang along. It worked.
These guys just don't hear it. J. Elefante once asked if I ever had singers working on a part and they sing it back to you in a totally different key and then ask "You mean like that?" They just don't hear it. I still like my job, though...

Yeah, it just strikes us as ODD that a singer (who hopes to be professional) has real trouble even hearing pitch! But it happens so often...

Other are often WAY too picky about pitch and don't' understand that it isn't too critical. Ask Dylan, Young, Morrissey, Plant... etc.

I've told this story on other boards, but I was doing a harmony vocal overdub session with a well-respected singer/songwriter and his guest artist, and the guest was having a dickens of a time trying to get the pitch right. The client and I knew he was nervous so we just kept encouraging him and telling him to take it easy until he felt warmed up and comfortable with his part.

After one particularly pitch-challeged take, we heard my wife yell from the hall outside the tracking room, "IT'S FLAAAAT!!!" She had parked there with a bottle of wine and decided to play assistant producer. The guest singer nailed it on the next take.

Lots of good stuff here.
Ive had some luck with:

The no cans/low volume monitor approach

I dont do the hand on the head thing but I do often hold one finger to my ear to get some bone conduction goin on.

Going with a bare mix/arrangement- sometimes just the bass and one other sound.

Boosting the high-mids and or the air freqs in the vox in the cans.

ANd... the biggest item ( I dont even think anyone mentioned it)...
Warm ups.
The voice relys on accurate muscle flexing to control the chords and the air flow.
Exercising in a range that exceeds the pitch range of the song to be sung makes the song seem relatively easy. Warming up /flexin those muscles is a must.

ALso,
KEY Selection.
The singers voice should rule this. Its amazing what a half step or so can do to bring things into control.