Back OT. I have hiked South Mountain a few times and got some of the caches. Vast majority of them (especially the referenced close ones) are on the National Trail and other marked trails and literally you can get them from the trail. There is no need to create any spider trails (and there are none as far as I have seen near the caches). There are a few caches which are on well used trails that are not officially marked but used by hikers/bicycles and so on. There are none I have seen that are after "area closed" signs.
Also keep in mind that while it looks 0.25 mi that is as the crow flies and this is a mountain park with altitude changes and quite a few curves in the trail between caches at times.
If you have seen any caches that are in closed areas or seem to be placed off trail and create spider trails I would suggest to contact our cache reviewer who in my experience has been very prompt in handling these type of problems.