@Maxmin I am aware that there are single sex school and co-eds compete with them for some students (not all, we know of plenty of students applying only to co-ed). Competition works both ways and single sex compete with co-ed as much as co-ed for competition for the respective gender cohorts.
What I do not follow is why a general statement co-eds needs to over offer more than single sex - surely it depend on the co-ed and single sex in question (desirability, location, etc).
The only issue in relation to offers from co-eds that I am aware of is that, in some areas of SW London where girl schools are quite prevalent, co-Ed might be offering more to girls because of the dynamics of the area and because the preference of girls for single sex is higher than that of boys for single sex. The HM at KGS was quite open about it - although he said that in their case it compensated the fact that girls tended to do better at exams. But this phenomenon is more nuanced than a general over offering for all coeds across the board.