On this side of the pond, cops are permitted to lie to suspects all the time, in an effort to secure a confession. This is often counter-productive, because if you solicit a false confession, it will come back to 'bite you' in the end. Police management and the local district attorney will not be amused by someone wasting their time in this way. Having too many 'failure to convict' cases is one way that the local DA may be asked to vacate their office, and find other employment. Often cases are dropped, or put in the 'inactive' file, because trying to prosecute may be deemed 'too risky' by the DA's boss. Remember that 'you only get one kick at the cat'. If you try someone for a particular crime, and they are acquitted, you can never try them again - even if postive proof becomes available (say DNA evidence), that conclusively ties them to the crime. Once you have convicted a police officer of extracting a confession by Illegitimate means, the flood gates open. Basically everyone that that cop ever had a hand in convicting of anything, is going to appeal, and it will cost the legal system millions. This sort of thing will REALLY get the cop & his superiors on the 'hot seat' for years.
I suspect that the cops in question thought they saw a resembance to the fellow from the video recordings, and were 'trolling for a response'. Had the fellow exibited some signs of guilt - running, or appearing very nervious, the cop would probably have indulged in more detailed questioning. Eyewitness identifications are nortoriously uncertain and inaccurate. This is one reason that more technical means (DNA, fingerprints, other forensic analysis) have taken over most criminal investigations. In normal western society, there are statutory limits as to how long police can question a subject. After that period of time, they either have to charge the individual or release them. I feel that your best procedure is to initially co-operate with the investigator. Do not volunteer anything, and if they start getting serious, just tell them you want a lawyer, and don't want to talk to them further without council - and stick to it!! They will try to get you to keep talking, but if you stick to your statement, they have to comply. Best of luck.