When playing in a band, one is said correctly tuned, relative to the rest of the band. Even if they are out of tune to the rest of the world, they will sound good. In this situation, the best tuner you have, will make you in tune, relative to the "correct frequency", but you will end up out of tune to the rest of the band (remember, we use a grand piano in this topic. You can't just retune an grand piano to your guitar).
It's strange you should mention jazz musicians...
All of the Jazz musicians I've come across are known to be the most anal retentive people when it comes to being in A440 pitch.
If you're out of tune, you're out of tune...there's no two ways about it.
Invest in a good tuner, it does not have to be expensive; just one which is accurate and tracks relatively well even in noisy conditions eg. stage or jamming sessions.
A good tuner is probably the single most important piece of gear for a musician.
Thats why i thank god i don have perfect pitch....i wont be able to watch a live van halen recording otherwise! in early days it is often known that anthony and eddie would just tune to each other....which would simply mean it would be just painful for someone who is anal retentive to hear......