DrMefistO, do you actually have a Teensy 3.0 board? If so, just turn it over and look at the bottom side.
The reality is the 24 pins on the edges of the board are much easier to access. The 10 other digital pins, plus 2 more analog, are only available at the bottom side of the PCB. In designing any product, there are always trade-offs. With Teensy, an important goal has always been small size. If those 12 signals came to the edges of the board, it would need to be 43% larger. The vast majority of projects do not need more than 24 pins. Just look at how many projects work with Arduino Uno, which has 20 pins. But this chip has those extra 12 signals. I put those pads on the bottom side so you can get access to those other 12 signals, if you really need them. There are also 2 more analog, and the voltage ref, on a 2nd row of pads.
There truly are 34 digital I/O pins. There's also 4 more analog input only pins, so really there's a total of 38 signal pins. But those other 4 aren't "I/O", since you can't use them for output and as inputs, they're only for analog.
It sounds like you might be unhappy with the product's description? That too is a design trade-off, with a triple goal. #1: provide as much info as possible, #2: keep it brief, mentioning only the most important info, and #3: show the product's selling points. Certainly the goal is NOT to mislead you or anyone. But on a summary page, there isn't room for every little detail. That's why there's reference section. This is common practice for pretty much all technical products.
Every Teensy 3.0 has that printed reference card included. It's full color printed on both sides, using those 2 PDF files. To see the info about the other 12 signals on the back side, all you have to do is flip the card over. Or if the real Teensy3 is in your hand, just look at the bottom side. Since there's no parts on the bottom, pretty much all the space that isn't pads for connections is printing to label everything.