The key point here is that while this is possible, it is time consuming and unnecessary. Identifying someone from a blood sample requires DNA testing which takes Months . Waiting a couple of days to get a proper search warrant for blood, and a Known reference sample is the correct way to deal with this. Comparisons of 2 unknown samples are likely to be inadmissible in court anyway. This story highlights two of the misconceptions of forensic science in the media.
Fingerprints can be, and are recovered from any surface the suspect touches.
The second misconception promoted by the media regards the speed of forensic analysis. On Homicide they had a story in which the suspect was leaving notes behind sketched with chalk. So of course they took chalk samples and rushed them off to the lab. Within hours they had identified the chalk. It should be noted that all the processing and testing in both these stories is possible and could be carried out on items of evidence.