As for the second paragraph: it is not an parallelism in the traditional sense, but as an shortcut in description of the design. To rephrase it in concrete terms: if you implement 128b block cipher as an two independent 64b wide SPN networks, you will not get the same security level as in 128b wide SPN network and the reason why is obvious from the SPN network diagram. (Compression function of hash function based on Merkle-Damgard construction is effectively an block cipher with somewhat large key)
In fact, the paper even mentions inverse of this in the context of the sketch of wider RIPEMD, where the sketch recommends some mixing between between the separate streams (particularly, exchanging one word of the state) between rounds, which the authrs view as enough to make their multi-collision attack infeasible.
In fact, the paper even mentions inverse of this in the context of the sketch of wider RIPEMD, where the sketch recommends some mixing between between the separate streams (particularly, exchanging one word of the state) between rounds, which the authrs view as enough to make their multi-collision attack infeasible.