I am experiencing the same problem. I have an Original iPad and a New iPad (both current on OS updates). After replacing an image for a web page, the new image shows up on Safari (and Chrome) but after I "Add to Home Page", the old image displays. I have performed all of the following to correct but no luck on my Original iPad:
1. Close all Safari Tabs
2. Clear Safari History
3. Reset Safari - Hold Power button and until slide to power off and then hold hold home button until Safari closes
4. Deleted the EVERY Web App icon on the Home Screen that references that Website
5. Settings -> Safari -> Clear History
6. Settings -> Safari -> Clear Cookies and Data (All Website Data should now be cleared
7. Stopped EVERY task in the multitasking list
8. Powered OFF the iPad
9. Stopped my Apache Web Server and cleared all logs
10. Started Apache Web Server
11. Started the iPad
12. Open Website in Safari and New image is displayed
13. "Add to Home Screen"
14. Exit Safari
15. Open Web App from icon on Home Screen
OLD IMAGE IS DISPLAYED
16. Viewed Safari Access Log and confirmed that the New image is retrieved as it is twice the sixe as the old image. Apache had 2 references to my image file the first resulted in 200 RC and 41232 file size and the second log line resulted in a 304 RC which means it had not changed and pulled from cache.
NOW I change the IP Address of my Apache Web server, open Safari and go to the new IP Address Web Site (that has all the same unchanged files, content etc.) and the NEW image is displayed as expected. I then "Add to Home Screen", close Safari, OPEN the Web App from the Icon on the home screen and the NEW IMAGE IS DISPLAYED CORRECTLY.
I would say this appears to be a bug and as a result the Bank I work for has suspended iOS based application rollout because this implies that sensitive customer data may be cached unexpectedly.
Please escelate to severe defect!