Late pays can be a sticky topic when it comes to credit reporting.
Some creditors have, in the past, been known to hold payments received on time until past the due date. While this practice may not be as common in today's credit world, it still does happen. When it does happen, more often than not it is unintentional.
Unlike most items, inquiries only stay on your credit report for 2 years. With regards to your FICO score, they are only considered for the first year, and afterward have little or no effect on your score.