Google more than ever prefers to index pages that offer quality within its indexes and many sites experience no profile indexing and this is because generally profiles are low quality and have pretty much the same values across the site with little change apart from Name: Nickname: etc, however this doesn't mean these pages can't be indexed or even give a page rank, and no these pages do not need backlinks to get indexed -
I've seen profile pages with many links not be indexed and this is normally because they are 'LITE' or 'THIN' as Google politely puts it. Stack Exchange flows PR into profile pages and many turn up on Googles indexing but many do not receive PR nor do they get indexed and this is because they offer thin content see: Many Stack Overflow users' pages have no Google PageRank and they are not indexed, why?
Many sites attempt to get users to provide as much Profile information as possible such as 90% complete and this is because they know the value of the data to the search engines among other reasons but maybe a another time, If you want your users profiles being indexed then you should ask around 200-300 words unqine text and you should notice these get indexed, but again.... This process takes time, if were talking thousands of profiles you can't expect to update one and see if it works because it can take Google months to come back to that page it once believed it was useless.
So summary, profile pages are useless to Google's index unless these profiles offer value, Bing won't even take a second looking ;)
Also in response of the other site having profile pages listed this could because they are treated differently by Google (Authorithy Wise) and Google believes the pages are more important, but it could be a mixture of reasons, end of the day you shouldn't see profile pages as adding quality to your site unless people provide the quality and then if they are indexed you know that page might of helped you in some way, 10,000 thin pages does not help sites in any way and panda doesn't like thin pages ;)