I don't have the expertise or credentials to conduct a proper title search to the level required to bind title insurance. I can eyeball the history of liens and deed transfers, and as Cameron points out I can identify key items that require additional documentation (such as tax liens or a divorce)... but nothing I can do is nearly as reliable as an abstract produced by a title agent.
I would never expect a Realtor to conduct a title search prior to submitting a purchase contract for mortgage underwriting, nor would I expect a Realtor to analyze a borrower's credit history or income documentation prior to accepting an offer. The Realtor's professional expertise and licensed activity lies in other areas.
Title searches are produced by licensed professionals because the of the expertise and education required to conduct the job properly. I would think the other agent would understand this, but with a pay check on the line, perhaps he/she isn't thinking as clearly as he/she should.
This might make me a terrible listing agent but I don't spend a lot of time with title issues at the time of listing. If there is something that I can see (divorce, foreclosure, recent improvements, etc.) that raises a title flag for me, we look into it, but we normally assume that title is fairly clear and if it isn't, we will be able to work things out with the title company as the transaction progresses. Either way, I never do the research myself, we have a title company handle that for us.
Tell the cobroker that it is as much her responsibility to do the research for the buyer as it is your's to do the research for the seller. You might consider starting a new thread with what title issues you are facing. Their are many agents who answers questions here and one just might have faced the issue before and have a creative solution for you.