Ancestry.com Texas Birth Index Question

I have a question about the Texas Birth Index accessed via Ancestry.com. I searched for my birthday (09/13/1969) and county of birth (Tarrant) and found 23 results including my own name and adoptive parents. A Search Angel (Terrie) sent me a birth certificate number for the one result that listed the baby's name as the last name of the mother (the actual index lists the name as "<mother's name> INF OF"). Unfortunately, the birth certificate number that Terrie sent me does not match the one on my birth certificate. She explained that that means that that particular mother is not a match. I tried to further narrow the potential matches even further by searching Ancestry.com for each of the remaining 21 babies' names. If I got any results listing a location where they have lived at one time or in a couple sad cases that the person is deceased then I know that that could not be a match. I also eliminated the Hispanic names as I have no Hispanic traits. Yes, I know that looks can be deceiving but I was just trying to narrow things down. I ended up with five names. So here is my actual question. Is it reasonable to assume that one of the remaining five search results is a match for my birth parents? That seems too easy. Thanks for any clarification. Shaun