Mr Dursley didn't see the owls flying around in broad daylight but ...
I don't understand why から is used in this sentence. What is the difference from writing 真っ昼間に?
Many usage examples of 真っ昼間 involve drinking alcohol during the daytime. According to this page, it is stated that it is typically used to describe an action or occurrence that is not normally done during the daytime, often with a judgmental (or surprised) tone. This definition is more in accordance with the use of から than に, as in 'from such a time as would normally be considered too early'. This includes drinking, sexual activities, burglary, etc.
真っ昼間から暗闇体験ができる！ One can experience darkness in the daytime.
ときどき二人で真っ昼間からパチンコ屋へ入っているそうです。They sometimes seem to go into pachinko parlors (even so early as) in the fullness of day.
Using に, on the other hand, does not have this implicit judgment about the hour that it is happening.
全裸で真っ昼にパレードに参加 Joining an all-nude parade in the broad daylight.
よく真っ昼間にどこかの山にのぼって、... Often climb some mountain in the middle of the day, ...
As neither parades, walking down the street naked, nor climbing mountains are considered regular nighttime activities there is no judgment or surprise about how early it is. Simply that it is happening in the 'middle of the day' or 'in broad daylight'.
In your example sentence, there is not so much a moral judgment, but more of an indication that this would be perceived to be an activity that is not expected to occur until the sun goes down. I don't see any problem with the translation provided, as most people understand implicitly that most owls are nocturnal and only fly at night.
I feel like if you say 真っ昼間から you are implying that the owls started flying around "from" midday. 真っ昼間に wouldn't indicate that they began flying around then, just that they were flying at that time.