Of course there's no requirement, but everyone knows that paying off a loan early can, in some circumstances[0], lower your credit score. Nobody is taking the time to look into your score and see why it was 810 last month and is 780 this month. They just use the 780 and move on, so it can absolutely affect the rate you get, and whether you get approved or not. No creditor is overriding a denial because they spent time investigating your recent score change.
[0] Usually the credit score is a measure of how likely you are to hold credit over time. It is not a "how good are you with money" or "how much money do you have" score, it is a "how likely are you to pay this back under the agreed-upon terms" score. Part of that score is the mix of different credit types, so if you pay off your final installment loan (e.g. car, house, private loan, student loan), your mix of credit types just went from N to N-1, hence a temporary, minimal drop. This is also why paying something off early can negatively affect it (in certain models, but I don't think this happens much anymore). This is always used by people to explain how credit scores are stupid and evil and idiotic and evil and stupid, but its effect is always overblown, and your score almost always rebounds within a few months.