What they seem to be inconveniently failing to mention is that the Euro, US Dollar, etc. are ALSO based on nothing, with nothing backing them (in so far as they are no longer have the gold standard or anything else specific actually backing these currencies, and they are free to print up more and more currency, which the US for one has definitely been doing.) Bitcoin at least has a strict limit on supply (scarcity). These groups also like to lump in bitcoin with the numerous (often scams) cryptocurrencies that may trade on a block chain, but are often just units that someone mass-produced in the hope to make a quick buck.
Note! I don't have any Bitcoin, I never have, and if I did buy/sell any I'd treat it like currency trading, not as some safe investment to do long-term investing in. Just pointing out, many of the criticisms the central banks have against crypto apply equally well to their own (as the crypto investors call them) "fiat currencies". Don't get me wrong, bitcoin *could* of course collapse, but so could the Euro or the USD (if those did, you won't see some "what's the USD worth?" value drop to 0, what you'll see is prices rapidly going up as the buying power of each Euro or USD drops off, a.k.a. hyperinflation.) Is that likely? Some of the economic policies taken by both the US and Eurozone, and the world bank, are troubling, but I doubt it's likely.
That said, I don't see Bitcoins dropping to 0 either, besides the bitcoin "true believers" and amateur investors (for lack of a word), there are now forex traders who are finding the foreign currencies too stable (profit is made by taking advantage of price fluctuations after all) and are investing and trading in a few of the largest crypto currencies *because* of the price instability; I think they alone may be enough to prop the price up now whether the banks want them to drop to 0 or not.
