The amount of people on site when/if it rains is super important. I remember in 2013, Thursday afternoon to early evening, approx. 10mm of rain fell (I was following in real time with models and radar app etc, the weather geek that I am...!). The site became muddy and slippery within a couple of hours, especially any grassy high traffic areas like The Park and major walkways. Not to 2016 levels, but enough to make it unpleasant. It pretty much all dried out quickly throughout Friday morning, but even 10mm can transform the site for the worse.
30-40mm when there's people on site would definitely cause issues. I believe the 2005 storm dropped something like 40-50mm early morning on the Friday, and was pretty awful for anyone that can remember it...!
But 30-40mm on Tuesday before the hordes arrive, especially if it's during Monday-Tuesday night, would hopefully not cause any problems. It's the thousands of repeated footsteps on the grass that seem to draw the mud up and transform the site into a sticky brown mess.