You need to enable "high quality" full screen scaling to get the benefit of turning pixel rounding off.
You normally would not want linear sampling on for pixel art games. Well it is an artistic choice but it is confusing the matter for now and is not related to what you want to achieve.
To achieve what you want with those textures and if you want smooth panning and zooming / scaling pixel art you need
pixel rounding off and
high quality scaling on
Point sampling would work great, unfortunately it breaks completely when used with zoomout or letterbox scaling; and the effect looks even worse than the one presented above.
Still no solution, but I've got some data. There seems to be an odd pattern between zoom and flicker&blur, check out (notice how 0.5 is the best performing zoomout) :
*flickering lines and blur is rated on an abstract 0-4 scale based on my visual input when looking at one TiledBackground object.