I've read that an effective dry brine takes 3 day on a thawed turkey, however, i read that you should not keep a thawed turkey for longer than 3 days?
Your question is somewhat unclear. If you are asking why there is a discrepancy: there is no reason for there not being one. Taste and safety are independent. If you are asking what you should go by, this is not a question we can answer. Choose whichever you prefer.
Raw turkey stays safe for 1-2 days in the refrigerator, no matter if it has been previously frozen or not (as long as it was kept safe while frozen). Source: StillTasty.
You can use a recipe with a 3 days refrigeration time or longer if you want to. It simply won't be safe. It may well give you a better taste than doing it for a short time.