It's an intractable tradeoff. A human count can be overseen, but as you noted, you can bribe overseers and overseer overseers ad nauseum, and in a national-scope election, someone with state-level resources could come into play. OTOH, a machine count can be subtly subverted beyond the scope of human senses. Heck, they may even come up with ways to corrupt the audit trails.
PS. The need for speed is so as to get the result in a timely manner, which can be important for parliamentary elections because there is no legislative activity possible between the dissolution of the old parliament and the forming of the new one.
Biting the hand that feeds IT
