The mechanic that is in-line with the lore is the initial 120 minutes. It also states there are alternative ways to extend your stay, but that does not involve the NPC's. Those NPC's caution against you staying for an extended time because they themselves have experienced detrimental effects to extended time in our world. Therefore, it just stands to reason that they would not willingly allow you to do something that would potentially put you at the same risk.

Go back and read it all again, and think about what they are saying and apply it to what they do. Their actions are in line with their words.