However, the fact that the alien does not accrue unlawful presence does not mean that the alien’s presence in the United States is actually lawful.
-Authorized stay is a better term than lawful presence in the case we discussed. Lawful presence means based on the law (specific law article,, etc.), and authorized stay mean someone (e.g. USCIS, CBP officer or immigration judge) allow you to stay even if it is unlawful.