Beams and Invisibility

[Charon]

The psyker twists and obscures the perceptions of his foes to the point that he becomes completely invisible.

The psyker doesnt turn invisible. He alters the perception of his enemies. Thats a complete different thing. So even if a Landraider would create a perfectly visible trail of falling trees, this evidence would go completely unnoticed/ignored. Works like the perception filters in doctor who. The stuff is not really invisible... its just completely ignored including sounds, smell,...

[Houghten]

You realise the perception filters in Doctor Who aren't nearly as potent as you describe, right? If the wearer draws attention to themselves (such as with loud noises or fast movements), they fail.

[Charon]

You realise the perception filters in Doctor Who aren't nearly as potent as you describe, right? If the wearer draws attention to themselves (such as with loud noises or fast movements), they fail.

Some of them, not all of them.
There are waeker ones (the one hiding the door to prisoner zero for example) and stronger ones (the one who disguised a ship as 2nd floor of a house and even concealed its destruction). Doesnt change the fact that the psi power doesnt turn anything invisible but makes everyone else completely ignore the unit.
Also I didn't say its exactly the same think but "works like". Another example could be Obfuscate from V:TM where low level Nosferatu are just ignored if they do no overly noticeable things while high level nosferatu kan literally kick you in the butt without you noticing anything but a sudden pain which must have came from a sore muscle or sitting too long on a hard chair.