"He tightened the truss rod all the way and the neck still isn't straight. He says I need a new neck."
The problem: your neck looks like like #1 and the truss rod is tightened all the way or your neck looks like #2 and the truss rod is loosened all the way.
The wrong answer: buy a new neck because yours is broken.
The right answer: Heat press the neck into looking like #3. (We'll talk later about why you don't want a dead straight neck in my next blog post).
Wood can and wants to bend
No two pieces of wood are the same. Some will take in moisture and react to temperature differences more readily than others. You can make two guitars from the same tree, use the same strings and tunings, put them in identical cases, leave them in the same room, and one of the necks may end up with twists while the other remains perfect. It's not your fault and it's not the factory's fault. Technically, it's the tree and Mother nature's fault.
The truss rod, on the other hand, is less forgiving, as it's made of metal. Unless exposed to very high temperature — much higher than wood needs to bend — the truss rod isn't going to change shape, or for this matter, length. So by the time the truss rod gets hot enough to change shape enough to change the neck bow, the wood would be less suited for a guitar and better for roasting marshmallows.
The guitar being heat pressed here is a Fender Telecaster (country of origin completely irrelevant). It came in with a truss rod tightened all the way but still with a nasty back bow. Here's how it looked coming into my shop. Notice how you can see under the frets. This neck is most closely resembles figure #1 from above. The small image below is a zoomed in view.
When bending wood, two things matter: heat and force. Heating the wood makes it malleable and flexible. Force puts the neck into the desired shape.
Before heating, it's necessary to ensure that the frets are glued in, or else they could pop out — unlikely, but still possible.
To heat the neck up requires two aluminum bars cut to the approximate length of the truss rod, which doesn't travel the entire length of the board. Between the bars is a custom heating blanket that can reach 300°F or more. Shims ranging between .010" to .040" are strategically to "bracket" the problem areas. Then the neck is clamped flat, or relatively flat with wax paper and cork properly cushioning and protecting the neck.
Next, the neck is heated up to between 110° and 125°. The temperature is checked every few minutes with a digital thermometer.
Too little heat and the wood won't bend. Too much heat and you can damage the neck or loosen up any glue, causing frets to come out, the fretboard to separate from the neck, or cause actual burn marks — the guitar may read 100° but the bars could already be hotter than 200°!
After the optimal temperature is reached, the heat source is turned off and the neck is allowed to cool off while still being clamped flat. To be safe, I like to let it sit overnight, although you could probably unclamp it sooner than that. Next, I put the neck back on the guitar and string it up. Since the truss rod was fully tightened before the heat press, the truss rod can now only be loosened, so a completely flat neck, or even a little upbow is a good sign. It may require a few runs to get the desired result, but it'll eventually get there.
Here's how this particular neck turned out after the heat press.
Voila! Your neck is as good if not better than new and you saved a few hundred dollars!