This event occurred in the US. In the US, enzootic (dog-to-dog) canine rabies virus has been virtually eliminated through vaccination and stray control programs, making wild animals the primary concern.
It is quite true, as @EMT_Jedi stated, that rabies is usually caused by an animal's saliva, usually introduced by a bite (e.g. rabid cats, raccoons, etc.) However, this is not true of bat-related rabies. There is reason to be vaccinated after any strange contact with a bat.
The most dangerous and common route of rabies exposure is from the bite of a rabid mammal. An exposure to rabies also might occur when the virus, from saliva or other potentially infectious material (e.g., neural tissue), is introduced into fresh, open cuts in skin or onto mucous membranes (nonbite exposure). ...Exposures to bats deserve special assessment because bats can pose a greater risk for infecting humans under certain circumstances that might be considered inconsequential from a human perspective.
How dangerous is a bat encounter? From a risk to benefit ratio analysis, they are very, very dangerous. On the one hand, not all bats are infected with rabies, and there are some risks to the vaccine (fewer with the new vaccine, though.) On the other, rabies is considered universally fatal, making the benefit of treatment high. Only a few humans (including Jeanna Giese) have ever survived the illness*; until these recent survivals, rabies was considered universally fatal.
During 1990-2007, 34 bat-associated human cases of rabies (as determined by identification of the rabies virus variant which killed the victim) were reported in the US: 6 cases reported a bat bite, and 2 reported a probable bite; in 15 cases, physical contact was reported (e.g., the removal of a bat from the home or workplace or the presence of a bat in the room where the person had been sleeping), but no bite was documented; and in 11 cases, no bat encounter was reported, but the rabies virus was bat-specific.
In other words: Of 34 deaths from bat-related rabies virus, only 8 (or 24%) were associated with a bite/probable bite, 15 cases (44%) involved touching a bat, and in 11 cases (32%) had no known exposure to a bat at all, but were caused by a bat.
Any encounter with a bat, even a dead one, must be evaluated for post-exposure prophylaxis.
In the case discussed in the OP, the person was previously vaccinated. The CDC recommendation (also verified by the state department of health's epidemiologist), is,
Previously vaccinated persons... should receive 2 vaccine doses, the first dose immediately and the second dose 3 days later.
(Previously vaccinated persons are those 1. who have previously received complete vaccination regimens (pre-exposure or postexposure) with a cell culture vaccine or 2. persons who have been vaccinated with other types of vaccines and have previously had a documented rabies virus neutralizing antibody titer.)
Rabies cases have occurred among exposed persons who received rabies pre-exposure prophylaxis and did not receive rabies postexposure prophylaxis, indicating that pre-exposure prophylaxis in humans is not universally effective without postexposure prophylaxis. In other words, it doesn't matter if you've been vaccinated or not, if you've been exposed - especially to a bat - you need to be treated.
Unfortunately, in the US, animal rabies is common, and ~23,000 persons/ year receive rabies postexposure prophylaxis (PEP). (It may well be higher, as no reporting mandate exists.) With the elimination of canine rabies virus variants and enzootic transmission among dogs, human rabies is now rare in the United States, with an average of one or two cases occurring annually since 1960.
In the US in 2013, of the three human cases reported, 2 were involved in organ transplants (raccoon rabies virus variant) and one was a Guatemalan (canine rabies virus variant).
In 2012, one human died from an exposure to a bat. He touched a bat under a bridge. He did not report a bite to a witness. He became ill while traveling, and died in Switzerland. A number of humans exposed to his saliva (including his Swiss caregivers) received PEP.
*Some people in high-rabies areas without the illness have been documented to have developed antibodies to rabies. The mechanism is unknown.
Human Rabies Prevention - United States, 2008
Epidemiology of rabies post-exposure prophylaxis—United States of America, 2006–2008
Rabies surveillance in the United States during 2013
Use of a Reduced (4-Dose) Vaccine Schedule for Postexposure Prophylaxis to Prevent Human Rabies: Recommendations of the Advisory Committee on Immunization Practices