[VMG]

A valid digital signature gives a recipient reason to believe that the message was created by a known sender, such that the sender cannot deny having sent the message (authentication and non-repudiation) and that the message was not altered in transit (integrity).

http://en.wikipedia.org/wiki/Digital_signature

The purpose of the blockchain is to establish an ordered sequence of transactions.

[lmm]

Sure, but no-one calculates digital signatures in their head. Your bitcoins are worthless without computer systems, and those computer systems are the subject of attack by thieves.

[VMG]

Sure, but this attack is not about that.

This is a DDOS attack on the integrity on the distributed database, which is very bad, but not able to spend Bitcoin that isn't yours.