Both statements are true. The data is real, the arithmetic is right, and the 14 point gap still does not mean what it seems to mean.
Pooled over departments A to F. A lawsuit-sized gap: if you only saw this, you would suspect bias.
Step 1 · your call
Remember, men lead by 14 points overall. Make a guess before you open the files.
Step 2 · open the files
Tap a department to see its numbers.
Step 3 · find the cause
Departments A and B admitted about 6 in 10 applicants. Departments E and F admitted 25% and 6%. Move the slider to give women the same spread of applications across departments as men, and nothing else.
Step 4 · what it means
This is Simpson's paradox: a trend in the combined data that reverses inside every subgroup, or in most of them. Women were applying in far larger numbers to departments that turn most people away (C, D, E, F took 93% of the 1,835 women's applications, against 49% of the men's), and those departments were hard for everybody.
That does not prove the university was fair. It moves the question: why did applications split along gender lines before anyone reached the admissions committee? The 1975 study in Science found that the pooled gap came from how applications were distributed across departments and, after correcting for that, a small bias in women's favour (as summarised by Wikipedia, see Sources).
The rule of thumb: before you compare groups, ask which hidden variable decides who ends up where.
datasets::UCBAdmissions (4,526 applicants to the six largest departments, 1973), opened as CSV from Rdatasets and checked against the R documentation, which gives the same totals (1,198 of 2,691 men, 557 of 1,835 women). The dataset is a secondary copy of the figures in the original paper.