If this is untrue they could easily be sued for libel/slander or who knows what else. Either case is easy to prove. someone should be suing someone unless they are cooperating in some way.
You don't sue if there is no chance of collection, and/or the damages don't exceed the costs of bringing action.
Sure you do. If they are a competitor that has sold you something and is now accusing you of theft of what they sold you the first thing you do is pick up your phone and call your attorney.
Besides, who says there is no chance of collection. BA claims to be broke, but it also claims to be hiring people, developing new chips and running around sponsoring conferences. They cry poor, but it's likely nothing more than bullshit so they can screw people out of the refunds they promised them would be sent in May, but are now being denied. If you look at the project they had a problem with the chip and had to go back for that and have had numerous problems since, although it hasn't added up to a ton more cost for them as they are not even doing the assembly themselves, so it's not like they have a factory full of people that they've been paying for all of this time and it is not as if they had to have components built 2 or 3 times. Probably should have, as their stuff is still burning up, but that's another matter.
Bringing an action would be fairly low in terms of cost, and if BA is in the wrong they would without doubt settle out of court for some amount plus costs, if for no other reason than to prevent their own bills from pumping up in an indefensible situation, so we're looking at a few thousand dollars to get a formal action started and very likely coming out ahead. I don't know what the laws are there, but in the US this would very likely be subject to a punitive and/or triple damages award, as if this claim of theft is false, they did it knowing it was untrue, and thus it rises beyond negligence to willful violation of the law, which is then subject to damages beyond simple compensatory damages.
And it costs nothing to file a police report. You can do it online in Hong Kong for nothing. BA claims to have done exactly that with respect to what they claim is a theft.