Your questions are among the most common asked in relation to HPV infections. Just yesterday I answered in great detail; rather than repeating it all, please take a look at that thread:
http://www.medhelp.org/posts/show/763292
As you will see there, my thoughts and advice are more in line with your urologist. However, I don't agree with the urologist's characterization of most gynecologists' approaches. A recent research study of providers' attitudes about partner notification for STDs showed that most gynecologists in fact talk to their patients about the sexually transmitted nature of HPV, and many (most?) advise referral or examination of partners. But I disagree, and so does CDC, which conducted that research study.
However, two caveats: First, the other thread and the CDC/gyn experience refer primarily to HPV detected in women by pap smear; and the context of the other thread is distant past partners, i.e. several years earlier. When a newly diagnosed HPV infection obviously was recently acquired -- as when new warts appear -- it is at least a courtesy, and some would say an obligation, to inform recent partners, i.e. those who might be the source of the infection and others who might have been exposed to it. It is true not much can be done, but many persons will appreciate being advised to be on the lookout, so they can see their docs promptly if warts appear.
Second, it is reasonable to consider the nature of the relationship. Most important, it's probably wise to tell current or future committed partners, e.g. when a long term relationship seems on the horizon, about past STDs. In the event such a partner later develops an HPV problem -- say warts or an abnormal pap smear -- it's generally better to have had "the talk" well ahead of time, and not in response to a new diagnosis and possible emotional crisis.
In summary, the main reason I disagree with your GP is his apparent black/white stance. At the same time, your urologist's attitude seems too cavalier. This is an issue colored in shades of gray, and one size does not fit all. Common sense about the nature of the diagnosed HPV infection, when and where it was acquired, timing, and the nature of the relationship all should influence a particular person's approach.
Inconsistent advice from various sources? Yes indeed. Frustrating? Ditto. But that's in the nature of the infection, as well as the rapid growth of knowledge, that naturally leaves some providers less informed than others, and which also fosters widely varying yet equally valid opinions.
So there you have it -- a fuzzy, gray-shaded answer to a fuzzy, gray-shaded problem!
Good luck-- HHH, MD