Try to avoid eye contact and conversation, and keep walking if approached making sure you have an exit and are not boxed in.
D4D I do think that is a bit of a stretch.
I have been here for 9 years and have never felt unsafe during the day.
Most black fella's and white fellas are very friendly and would nod and acknowledge you like any smaller town throughout Australia.
There are problems with alcohol abuse, and anti social behavior, which are rarely seen through the day. In the same way I wouldn't walk the back streets of any city at midnight, I wouldnt do it here. Tourist cars parked in the CBD overnight are often a target for thieves.
Problems at any of the caravan parks is a bit unusual.
Alice has a lot to offer, some great tourist attractions (RFDS, Transport museum, Desert park, old telegraph station to name a few) great bike trails (both paved and some of the best single track MTB you will find). It is a great place for exploring the east and west mac's, Rainbow valley and Owen Springs. Numerous supermarkets, some great cafes (reasonable coffee but not always melbourne standard)
By the way john laws was on at work that day, many of the voices recognized were using fake names, I wouldn't put too much faith in talkback radio for giving the best summary of any subject, you get 2% of the extremes and not much of the real 96%.
Have a great trip.