A report due next week from the UK's policing watchdog questions how the HET inquired into killings by the Army in Northern Ireland.
Meanwhile the Bloody Sunday families are angry that HET staff are being re-assigned to look into those shootings.
The report from Her Majesty's Inspectorate of Policing was requested by the Policing Board and is likely to be highly critical of the historical team.
It will ask if HET did enough to properly investigate Army killings, and if it was robust enough in how it dealt with the soldiers responsible.
They could find all the resources they needed for G8. Why can they not find it for those families that have suffered as a result of the conflict?
Gregory Campbell MP said: "It may well be the case that the Chief Constable is saying 'however thinly I spread his resources about dealing with the past - whether it's the HET or Bloody Sunday - I'm not going to satisfy everyone'.
"Now if that's his assessment, he's very probably right."
Investigating the past is crucial to the Bloody Sunday families' campaign. They were told last year the PSNI was starting a fresh murder investigation into the shootings.
Now they're dismayed to learn that around a dozen experienced HET staff are being transferred to this inquiry.
Conal McFeely from the Bloody Sunday Trust said: "We're actually so annoyed and angry that the Chief Constable has made this decision, after publicly saying one year ago that he was actually setting up this investigation, that he would put the resources in place.
"To find out through the back door that in actual fact he hasn't put the resources in place is an insult to the families."
Mark Durkan, SDLP MP, said: "They didn't indicate that it was going to be at the risk of switching significant numbers of personnel from the HET and maybe then stopping ongoing inquiries or planned inquiries."
There are suggestions a major shake-up of the HET could be about to happen - even that Army killings may have to be re-investigated.
The report is to be presented to the Policing Board next Wednesday.