The reader knows that Geralt had to bite her - Velerad certainly didn't. When they arrived in the morning, the saw the princess, with a bite on her neck, and the witcher, with his neck slashed. One should remember that witchers (well, at least Geralt) are notoriously secretive about their ways of dealing with monsters.
‘You’ve had a fair amount of experience, I dare presume?’
‘Yes, your Majesty.’
‘I would love to hear about it.’
Geralt bowed even lower. ‘Your Majesty, you know our code of practice forbids us to speak of our work.’
And why would they? All sorts of idiots would go and try getting rid of monsters themselves. There would be less idiots, sure, but also less people with coin.
Geralt only said he had to spend the night in the crypt, without elaborating too much. To Foltest, however, he had told that there may be complications:
‘I confirm, your Majesty, that the spell might be reversed. And, unless I am mistaken, it can be done by spending the night at the palace. The third crowing of the cock, as long as it catches the striga outside her sarcophagus, will end the spell. That is what is usually done with strigas.’
‘It is not simple. First you have to survive the night. Then there are exceptions to the rule, for example, not one night but three. Consecutively. There are also cases which are . . . well . . . hopeless.’
But he hadn't told this to the others. They had no idea what exactly was going to happen in the crypt, but based on their previous experiences, they would assume that Geralt wouldn't subject himself to more danger than absolutely necessary, and they most surely didn't know the princess would be feral for some time even after the curse was lifted.
See, the witchers aren't known for being sentimental . It is believed that the procedure that gives them their powers also strips them of emotion (and this may or may not be true). It was made clear quite a few times in that story that the witchers who tried this previously did not wish to risk their lives even more by trying to undo the curse.
But it also seems that Geralt's decision to check her wasn't the wisest one even by his standards - Nenneke remarks in "The Voice of Reason II" that he shouldn't have gotten himself injured, and that he should have been more careful:
‘It’s terrible! To let yourself be slashed like this by an ordinary striga. Muscles, tendons – she only just missed your carotid artery! Great Melitele! Geralt, what’s happening to you? How did she get so close to you? What did you want with her? To mount her?’
Most likely this verification procedure wasn't exactly standard, and was done by Geralt because he emphathised with Foltest.