According to Manual of Forensic Emergency Medicine by Ralph Riviello at page 118:
There are many enduring myths and misconceptions about the hymen. It is essential to note that first coitus does not result in any hymenal injury in a significant percentage of patients. Tampon use, sports, and prior pelvic examination do not cause hymen injury
The book cites "Hymenal findings in adolescent women: Impact of tampon use and consensual sexual activity" Journal of Pediatrics vol. 125, pages 153-160 as the source of this information.
The article specifically states:
the presence of these complete clefts was not related to participation in sports
The article further finds:
81% of examined females who reported not being virgins had completely cleaved hymens. (This means that it can not be determined that someone is a virgin, because even if she is not the hymen could still be intact.)
Only 11% of tampon users and 5% of pad only users who reported being virgins had completely cleaved hymens. (The authors did not find this to be a statistically significant difference but "Can tampon use cause hymen changes in girls who have not had sexual intercourse? A review of the literature" Forensic Science International vol. 94 pages 147-153 explains that depending upon criteria, this could be a significant difference).
Overall, one can see from this data that there is about a 19% chance that a young woman can have an intact hymen despite not being a virgin; and a 5-11% chance of having a cleaved hymen despite being a virgin.
The review article above similarly says 16% chance of an intact hymen despite not being a virgin; and 10% chance of having a cleaved hymen despite being a virgin. It explains that the possible reasons for hymen cleft beside intercourse are: congenital irregularity; penetrative injury as a child; insertion of tampons; insertion of objects (such as vibrator); or digital penetration by either self or a partner.
The review concludes:
Discretion is indicated when physicians are required to testify, remembering that both the sexually active and the never-sexually-active groups of adolescent girls include some with hymen clefts.
So, no, examining a hymen is not a reliable way to determine virginity.
Going back to the issue of sports, since a bounty has been placed with a request for more information on this topic:
In Child Abuse: Medical Diagnosis and Management (2001), Reese and Ludwig editors, quoting from pages 235-236:
The hymenal membrane is recessed in the vestibule, protecting it from direct trauma; hence the implausibility of injury to the membrane from athletic activity such as bicycling, horseback riding, or gymnastics. The common misconception that the athletic activities cause injury to the hymen has no scientific support