I don't *think* there is some intermediate cookie/value being stored here, here is what happens:  

1) Attempt to link URL  
2) Resulting error (file too big; must be 100x100)  
3) Resize image in MSPaint. 
4) Attempt to upload from "Choose File". Click "Change Avatar", because nothing else is happening.
5) Get the error:  

 Please correct the following errors before continuing:

• The URL you entered for your avatar does not appear to be valid. Please ensure you enter a valid URL.
  

6) Continue to get get the same error even if you reload the page or come to the page from another URL again.