There is no need to have two BBR networks. This is very simple. Normal (standart client) use checkpoints, to speedup blockchain loading (every currency have it, including bitcoin). Under checkpoints some checks are skipped. This based on idea the users trust developers and their checkpoints.
But, if some "new user" don't want to use checkpoints(don't trust developers), and want to completely validate(mathematically) whole blockchain from genesis block, then he build hi own manual client(or provide some command line params, depends of implementation) and completely validate whole blockchain. In BBR can do simple the same just by taking this complete version of blockchain, and do this verification for every transaction.
In ~99.8% of blockchain-based cryptocurrencies you can verify the entire chain by: 1. Retrieving the entire chain from the p2p network, ensuring that you have the correct chain with the assumption that you are able to connect to at least one honest peer, 2. Verifying that no blocks have ever been changed by checking block and tx hashes, and 3. Verifying that chain of transactions from the genesis block is valid (with checkpoints disabled).
Boolberry:
1. Can't do #1 because the chain doesn't exist on the p2p. You would have to use (i.e trust) a web site.
2. Can't do #2 because the tx hashes don't include signatures.
3. Can do #3 predicated on the assumption that nothing has gone wrong with #1 and #2
Certainly you can see a degree of trust has been added here (#1) and the chain of steps that is normally used for trustless verification is broken in at least two places (#1 and #2).
As I have said before, I don't know that this is necessarily a bad trade off, but it is a different trade off. What is frustrating about it is not that Boolberry has decided to do something differently (experimentation and diversity and choices in the marketplace are great). It is that Boolberry aggressively portrays its changes unambiguously as "improvements" or "fixes" when they are actually trade-offs. This confuses people and causes them to then ask us why we are relying on an "unimproved" solution when in fact we have simply made different tradeoffs.
A very similar argument could be made about XCN, except that XCN is much more explicit that it is making a trade-off in order to achieve certain goals, and doesn't run around saying "XCN fixes Bitcoin flaws."