I agree, it says "Nights between 2/1 and ..." the night of 1/31 is not between the dates, checking in after midnight makes no difference, it is still the night of 1/31. It seems reasonable to me that February 1 starts at noon in a hotel sense, if you look at it the other way and were asked to leave at midnight you wouldn't be too happy, I for one assume my booking for 1/31 would run up until noon on 2/1 so why shouldn't the booking for 2/1 start at noon?