Publishing everything on a blockchain means that everybody who's running a node has access to a copy. If confidentiality of communications is an issue, this may as well be a data breach with a few more steps. Also, how does giving everybody running a part of or monitoring the blockchain equate with "control over personal data?"
Centralized control: Only one entity can see it. Blockchain: Lots of third parties run a node, so every node can see it.
Each channel has a separate ledger: That makes surveillance of a particular communications channel much easier. Thanks. Also, each user has to have a keypair; great for pseudnonymity, lousy for repudiability.
Messages cannot be altered but they can be audited to prove their metadata. Did they learn nothing from the Obama administration? At this point in the paper I can't shake the feeling that this is a deliberate effort to invert all of the properties of privacy.
Smart contract: Yay, more deliberately memory unsafe programming. I guess they never played with Core Wars as kids, either.
An attacker would be unable to breach the network: An attacker would just have to stand up a node. If channels are side ledgers on a blockchain, and the network assumes that nodes can come and go (which they all do, as far back as bitcoind), any node can join, say "Hey, I'd like to join this channel," and get at the very least a pointer to the side ledger for that channel.
Long-term storage of communications is dangerous, mm'kay?