In response to your first sentence, here are a few citations that I believe support the non-neutral connotation of "putative".  On the chance that these are copyrighted, I supply here only the URLs. 
    
 http://www.alphadictionary.com/goodword/word/putative 

 http://www.yourdictionary.com/wotd/putative 

 http://wiki.nwtresearch.com/%28S%28ic0a2l455xdf5v45zxuxva55%29%29/Default.aspx?Page=glossary&NS;=&AspxAutoDetectCookieSupport;=1 

 http://law.yourdictionary.com/putative 

 As a linguist, I suspect from your writing that you and I do not share the same native language  (mine is American English).  If this is so, it is not surprising that we would not share the subtleties of connotation.  

 I agree with your last suggestion.