See also the story of Khujjuttara which shows this inability of sotāpannas to hide bad deeds.
Khujjuttarā, in her daily purchase of flowers for Queen Sāmāvatī, usually bought only four ticals worth of flowers and pocketed four ticals out of the Queen’s daily allowance of eight ticals for flowers. But on the day she became an ariya (as Stream-Enterer), Khujjuttarā had no mind to steal the money entrusted to her and bought eight ticals worth of flowers, which now filled her basket. Queen Sāmāvatī, seeing an unusually large quantity of flowers in Khujjuttarā’s basket, asked her: “Why dear Uttarā, you have such a big basket of flowers today, unlike the previous days! Did the King increase my allowance for flowers?”
Khujjuttarā, as an ariya, was now incapable of telling lies, and so confessed her previous misconduct. The Queen asked her: “Why, then, have you brought such a big quantity of flowers today?” And Khujjuttarā replied: “Because I do not steal the money today. I cannot do so because I have realized Nibbāna. I have comprehended the Deathlessness, after hearing the Buddha’s discourse.”