It very well may be an award ticket, in which case, everything you say is true! If KL isn't offering any seat for awards on a particular flight, it just won't show up, but searching by schedule - not price, should show whatever is available.

AF - fuggedaboudit! I go to TXL frequently, and, for PAID tix, if I try to do a multi-city search with a stopover in Paris, the CDG/TXL (or reverse) segment ALWAYZ routes via AMS on KL - not nonstop - and goofs up the pricing. Award tix, for some insane reason, DOES show the AF nonstop flights from CDG/TXL!

Why is DL's online relationship with KL better than with AF? - - - I guess that's a WHOLE OTHER thread!