Probably not too far off though. It was likely a capsule loaded into the straw at or above the joint of the straw. If he carelessly loaded a straw with a poisoned capsule into the drink, he'd risk the capsule falling into the shake and dissolving, thereby ruling out his apparent suicide ploy. So instead, he held it by the joint itself, despite the crinkles beneath his grip making it harder to insert the straw. The poison was never in the shake itself, nor had it dissolved before it could mix in with the backwash.