Brown Flesh?
ronfaneuff,
From what I can tell from your description, you are having the 'brown flesh' appearing on the fruit/apples themselves, and not the tree. For if this 'flesh' were showing up on the tree, I have no idea at present, however, if the problem is visable on the fruit, I can provide the following.
Chances are your trees are exhibiting 'Apple Scab', which affects collective groups of apples, crabapples, Mtn Ash, pear, etc. This is usually a problem in areas of high humidity and moderate temperatures.
The impact on the tree is that it reduces the quality of fruits and yield.
The signs and symptoms of apple scab are lesions on leaves and fruit with velvety olive brown masses of conidiophor & conidia (fungal growths), which would represent/resemble your brown flesh. Chlorosis and death of tissues, corky seals on fruit, bumps on twigs and curled or puckered leaves all represent a possible infection. The fungal spores travel through air currents or water, such as rain, for the conidia.
The control of apples scab is two-part. Naturally, resistent varieties, dry weather, earthworms and litter decomposers that degrade leaves and so reduce overwintering fungi, and natural composting seem to control the disorder. Chemical control is as follows. From first rain after bud break, spray every 5-7 days (more often if it rains) until petal fall, then 10-14 days several more times. Must keep young tissue covered with fungicide. If infection occurs, spray continues throughout the season. Chemical are preventative, not curative.
For best results and an accurate prognosis of the disorder, you should consider contacting a local arborist that could aid in your problem. Chemicals can be dangerous, therefore, having a qualified applicator do the work, makes the homeowner's life much safer and more relaxing.
I have added this attachment to give you an idea what the 'growth' really looks like.
Hope this was informative and helpful!
Shane Freeman
PS: If this wasn't a fruit flesh disorder, please ignore my gibberish.