So I'm pretty a similar problem could exist. If to accept a proposal we only need 3 nodes, not a majority, and we manipulate network latency in arbitrarily bad ways, a similar split brain could occur. Basically, you could commit the same transaction twice under different proposal numbers.
Consensus is not about transactions, it's about agreeing on a value (a single value, strictly speaking, unlike atomic broadcast, which is about agreeing on a sequence of values, although people often identify the two). But anyway, your argument is not in any way concrete - try to come up with a counterexample. Having thought about it more, I am confident that the author's system is correct (in the sense that it always preserves agreement).
Moreover, the leaders are lease-based in the author's proposal, so I believe that what he describes correctly solves consensus. However, his proposal doesn't really give much of a resilience improvement over the original Paxos, since the system, in the worst case, tolerates only 2 failures (leader + one more process), same as a 5-process Paxos. Nevertheless, an interesting idea, one that I don't think I've seen elsewhere.