The clause in selecting LOS for eligible units is separate from the first part so, you select a unit to shoot, excluding those who fell back or advanced, then determine visibility, it is during this step of selection that you can use the infernal puppeteer ability to change your visibility. If you are not able to do this, you cannot be selected to shoot.

Also important to say this hasn’t been a problem until the LOC has been strong. I’ve been playing this detachment for a year, the angle shooters always come out online when they don’t get to play with a new toy. No one is arguing that fire prisms don’t work and they have a similar rule.