I think twitter is better with focusing on their core competency of providing real time information rather then being side tracked into something very different.
Apple's stake makes good sense because offers both backups and decreases reliance on others. For Twitter it gurantees a medium/eyeballs and for Apple content.
Twitter already has good anti spam algorithms and for this case they should be able to determine the quality of accounts and the quality of the tweets as well: age of an account, diversity of the tweets, hash tags, verified accounts, account linking to 3rd parties, re-tweets by other 'good' accounts, etc.
I think that such an offering would only extend and enhance their current competency since I'm already using Twitter like I used to Google to search for real time info. But I like Twitter to become better, more advanced and more relevant in search. I want to find the information referred to in tweets (blogs, news articles, videos, charts, etc) not only sorted by time, but sorted by quality as option. Hundreds of 'opinion' tweets with no links are less valuable. I don't want to wade through them.
Perhaps this is one of the reasons why Twitter decided to end the availability of their feed through Google Search?
I do agree with your point about generally in having a more realtime and relevant serach engine. But I think instead of twitter some one working across networks would be in a better position.
bit.ly is going in this direction with its redesign and rt.ly and social sharing widgets like Addthis and Sharethis would also have a very good view of realtime data. That they could use.
The only advantage I could see with twitter is if they do sentiment analysis of the tweet text and then understand relevance. The context they have available could be akin to how google bot uses link title and anchor text but with 140characters more focused.
Twitter ending availability I think had more to do with google clearing space to forthcoming integration of g+