This isn’t the case with all tanks, which I’ll outline below;
Glass
Now with glass tanks, all of the pressure is actually applied and spread to the corners of the tank (which is why you have tank stands that only hold the tanks on the corners fully). Placing mats underneath aren’t recommend since it can shift weight over time, and apply all of the pressure from the corners to other parts - which under pressure/tension, will crack the glass.
Acrylic
Aryclic tanks actually spread the weight out from the bottom to the sides. These must have a completely even stand/bottom, where any imperfection on the weight being distributed on the tank can cause some unevenness and will put more water pressure on other aspects. Since it’s acyclic, it won’t specific break, but it will cause for the sides to bow outward more where there is uneven weight and can cause for the acyclic to deform over time (and thus causing for a weak spot where it will break at - but extremely rare).