Yes. That is what should happens because that is what happens during a murder investigation. The suspected murderer is allowed to walk around while a lengthy investigation goes on. Once they have enought evidence... THEN they arrest the suspect. Why do you have a double standard against accused rapists especially when it is well known that perhaps half of all rape claims, perhaps more, are false allegations that can and do ruin people's lives... and not just the man... his family too. Why are you OK with this?
It MIGHT happen that way depending on the situation and circumstances.
Here are a few different ways in which our system works - THESE ARE ALL APPROPRIATE depending on the specific circumstances:
1) If someone came up to the police in New York City and said 'that man over there just tried to kill me' do you think they'd let that guy walk around for two seconds before taking him into custody? Of course not. In this type of situation the police are more than likely to take the suspect into custody - immediately. While in custody he will then be initially examined / question / evidence collected as necessary to determine if he can be CHARGED.
My state has 48 hours in which to CHARGE someone AFTER they've been taken into custody.
2) If someone is accused of having JUST committed a heinous crime, the police might stop the person and question them where they stand. The classic 'questioning the witnesses and other people in the vicinity about this reported incident'. Now IF the police find there's some sort of concern or validity to the claims, then they will take the person into custody.
BOTH 1 and 2 depend on factors such as PUBLIC THREAT and VALIDITY OF THE ACCUSATION. If someone's carrying around a bloody knife, for example, or 5 seconds from boarding an airplane to thus escape an alleged crime are two examples in which the situation might warrant detainment while being investigated further.
3) When the police receive a report that someone has possibly committed a heinous crime and they DON'T arrest them immediately, this is because there isn't evidence enough that the person is a threat. OR they're not too sure that this person is an actual suspect. Such as if a body is discovered and someone says 'well John did it' - they'll have to do a bit more investigation before being able to take John into custody.
#1 is the murder-example equivalent of the situation that happened. She claimed 'that man over there just raped me' and they decided that given the situation they were going to take him into the station and look into things while he was there.
What's with everyone? Yes - in the US you can IMMEDIATELY be taken into custody and detained WHILE it's then investigated! I guess a lot of people just have ZERO experience with the way the law actually works in these various situations. So this notion that in the UK your rights are worthless and *chest thump* we're not that barbaric here . . . well obviously that's just bull****.