There have to be two elements for lawfully arresting someone, and taking away their liberty
1)
Suspicion, that an offence may have taken place. (note, suspicion is a very low level thing, there is no requirement for a
belief that an offence has occurred.
2) Belief that the arrest is
necessary (As opposed to dealing it with other means, such as voluntary interview). This is referred to in policing as the "necessity test" and at least one of a few criteria have to be met, for example
- protecting a child or vulnerable person
- preventing harm or injury
- preventing loss or damage to property
- because it would make the investigation prompt and effective, for example, if the suspect needs to be secured there and then to preserve forensic evidence...
and so on.
In these circumstances, someone has died. Ok they might be a shoplifter - but, someone dying during a physical altercation, is a serious matter, criminal or otherwise. Therefore, the other party in the struggle (in this case the security guard) will have been arrested on "suspicion" of the killing (eg, there is some chance he may have caused it by using disproportional force) etc - and the necessity test will be met because they will need to preserve evidence.
Someone being arrested on suspicion, does not mean the police believe the person is guilty. Arrest is simply a process which sometimes needs to be used as part of an investigation (an investigation which may well go on to clear the guard of any wrongdoing)
Remember that when someone is arrested, police officers are an impartial body and are compelled to investigate in an unbiased manner - this means they are obliged to pursue all lines of enquiry that may point to someones innocence, as well as their guilt
