In this case "Don't know" certainly equals "No go", since if it doesn't show a connection you won't find out about it. I also have to disagree with the reason you give for this behaviour (having also just double checked that nothing has changed on the DB website). It shows the connections from Berlin to Amsterdam if you click on the option to take a bicycle, even though you can't book the cycle place online.It is not so much "no go", more like "don't know". You cannot reserve a bike space on Belgian IC trains, and you cannot purchase a Belgian bike ticket on the DB website, so DB do not include information on bike provision on Belgian trains.
On the other hand, if you try for Aachen to Brussels (with bike), it'll show you a 6hr connection with several changes (via Nijmegen in NL) even though it knows of the 2hr connection via Walkenraedt (which shows up if you unclick the cycle option, even though cycles are carried on this connection).
As implied above, it also shows connections on Dutch ICs, even though, just as in Belgium, cycle places are unbookable and the cycling ticket for the journey is unavailable on the DB site. The lack of purchasability hasn't prevented the presentation of the information about connections for the NL, yet something has for BE.
Clearly the technical reason is that the data regarding bikes on Belgian IC trains has, for whatever reason, not been entered into HAFAS (or whatever it's called nowadays), but the end result is that the DB website can't be used as a solid source for taking bikes on non-DB trains, particularly outside of Germany, and travelers with bikes would do well to, as you suggest, use the railways website of whatever country/company you want to travel through/with.
PS As yet another tangential aside, the Man in Seat 61 has also started including information about bike carriage to and between European destinations - haven't checked for a while so don't know how up to date or comprehensive his information is: https://www.seat61.com/bike-by-train.htm
PPS I like the picture - nice cycle places for an IC, Britain and Germany (et al) should learn from that!