How to get a very tight tire back on the rim? I needed to change the tube as a consequence of a flat tire and I am in the situation that it's just impossible to put the tire back on the rim.

In almost ten years of experience with road bikes and MTB, I never experienced this.

I tried to use any possible tips, for example from the question How to get the tyre back on to the rim easily?

Every time I try, I end up pinching the tube and it's just impossible to put the tire in. How can I fix this? 

I am hypothesizing crazy things, like: dilatation of the rim, need of industrial tools, ... 

Edit (to address Neil's question): the troubles are given by a 700x23c tire on a 700C rim of a fixed gear.
The above video shows how to fit a tight tire / rim combination. Although it shows the Marathon Plus tire, it applies to any tire.

The crucial point he makes on the video is that the tire bead doesn't stretch and is the limiting factor in getting the tire on. Thus you need to push the bead into the well of the rim on the sides opposite to the last bit you're trying to get on. Doing this gives you the room you need to get the last bit on.
The extra room will make it easier and you will be less likely to pinch the tube. You can use straps to hold the tire in place if you need to.

I have the Marathon Plus tires and it used to take me an hour of frustration and sore hands trying to get them on. Using the technique in the video it takes me 5 mins like any other tire.