“Eat foods that spoil (just eat them before they do)” means that ones should eat fresh food, not food that is overly processed for a long shelf life.  Fruits and vegetables spoil.
 
The saying “eat foods that spoil” (or “eat food that spoils” or “eat foods that goes bad”) has been cited in print since at least 1968.
 
“If your food can go bad, it’s good for you. If your food can’t go bad, it’s not good for you” is a related saying.
 
     
18 July 1968, New Orleans (LA) Times-Picayune, sec. 6, pg. 9, cols. 2-4:
Buy Colorful Vegetables, Expert on Health Urges
Spinach Not Very High on List, She Says
By CORNELIA CARRIER
(...)
“Eat foods that spoil easily but before they spoil, if you want the nutrition,” she (Mrs. Margarita Wagner—ed.) suggested.

19 April 1976, North Adams (MA) Transcript, “Nutrition authority Ellis speaking at Williams,” pg. 2, col. 4:
He says his motto is “try to teach people to eat foods that spoil before they spoil.”
(William A. Ellis, a retired osteopathic physician—ed.)

Google Books
The Simple Living Guide:
A sourcebook for less stressful, more joyful living
By Janet Luhrs
New York, NY: Broadway Books
1997
Pg. 250:
Remember this important rule of nature when shopping for your food:Eat only those foods that spoil, rot, or decay, and eat them before they do. When you eat foods that spoil and decay, you are eating real, unadulterated food. That’s what real food does: It spoils and decays and goes back into the earth for another round.
 
Google Books
Cracking the Metabolic Code:
The nine keys to peak health and longevity
By James B. LaValle with Stacy Lundin Yale
North Bergen, NJ: Basic Health; Enfield: Airlift
2003
Pg. 338:
My mentor, Dr. Alexander Wood, always said, “Eat foods that spoil, just eat them before they do.” It is so true. Foods that spoil are foods that support life.
 
Hexus
rajagra
20-03-2005, 05:09 PM
There is a less well known saying: Eat foods that spoil, before they do…
 
Google Books
Real Food:
What to Eat and Why
By Nina Planck
New York, NY: Bloomsbury: Distributed to the trade by Holtzbrinck Publishers
2007
Pg. 81:
Remember this rule of thumb: eat foods that spoil — but eat them before they do.
   
Google Books
Live Without Pain
By Simon King
Naturality Press
2008
Pg. 128:
Eat food that spoils, rots, or goes off, especially for breakfast. Cereals don’t do any of these, nor can they be grown. They are dead and destructive to your health.

Here & Now
Tuesday, November 1, 2011
Chicago Teacher Gets ‘Fed Up With Lunch’
(...)
COMMENTS
Clara 1 day ago
Eat more RAW foods as Nature intended. As the old saying goes: eat foods that spoil, but eat them before they do.
Its all about getting enough ENZYMES into the body. Without them, little gets metabolized.