Foxes do go out in daylight. I see them every day, several times a day here. They pass through my garden and the Cubs come to eat dropped bird seed at my feeding station several times a day. When I worked in the town, we often saw foxes in the streets, though more often in the mornings than afternoons. And when I used to walk my dog in another county, up the hills, we could guarantee to see a fox cross the path at the same time every day. I watched a fox take a lamb at lunch time on our hill when I lived way oop North and managed to rescue it, and holidaymakers frequently took photos of foxes in daylight. I have quite a collection of such snapshots of my own.
As for cats..a fox met my cat in my garden and all I was left with when the noise died down was the bell of his collar. I was in the shower when it started so too late by the time I got downstairs.