They are accurate because the scale of the map changes. The map is interactive. It's been demonstrated many times in this thread that the interactive maps have a sliding scale.
Of course the scale changes but that doesn't fix the problem. Do you understand that if you do the experiments you suggested, zoom to Alaska so it's filling most of the mapquest window and zoom to Mexico so it's filling most of the mapquest window, that shape that you see for Alaska and Mexico is not their actual shape despite the scale in the bottom corner changing? Because there is no 2D representation of those states/countries that is not distorted. You have to stretch it or squash or distort it in some way to make a 2D representation. And the bigger the area you fill the screen with, the greater the distortion. While it's true that if you zoom right in to the highest level, the distortion becomes insignificant for practical purposes, that does not make it an accurate map.
Edit: Just to clear this up once and for all, I've used Mapquest and put in four Australian cities (Broome, Cairns, Perth, and Sydney) and then taken a screenshot. Distance between Broome and Cairns on the screenshot is 536.54 pixels (using the measure tool in Photoshop), in freemaptools, it's 2497.396kms. Distance between Perth and Sydney on the screenshot is 806.68 pixels, in freemaptools, it's 3290.287kms. So the former is 4.6546 km per pixel, the latter is 4.0788 km per pixel. In other words, km per pixel for Broome and Cairns is 14.17% greater than km per pixel for Perth and Sydney. I've also included a screenshot of the shortest distance between those points on freemaptools. It should be obvious that the bottom line is slightly more curved than the top. This is also another way of visualising the distortion on the map. Regardless, if it was possible to have a 2D representation of Australia, it should be possible for the software to make both of those straight lines and they would represent the distances accurately. But it's not. Also, if this was the case, pilots could also throw away their great circle mapping tools for domestic flights within Australia because they could use this amazing, accurate 2D map. But they can't.
Feel free to check my results.