Yes, Belize City on the south side of the Cannel has a high murder rate. As a policeman for many years in Canada I got to see that real stats for cities, and parts of a city. Stats are reported on a per/capita basis. Since Belize City is small, a bad area of the town skews that stats, and certainly does the same for the whole country.
If I were to pick a few bad areas of Edmonton Alberta, or any other larger city in Canada or the USA I could get huge numbers of murder rates.
Just because you read of murders in the newspapers does not mean it is a dangerous place. Read your local papers in Canada, or USA if you live in a city. You will read of murders, stabbing, serious assaults. Most people just ignore them because they feel safe for what they are doing. For 15 years I walked to and from work in the highest crime rate area in Edmonton. This was at all hours of the day/night. There was at least one serious assault if not stabbing / murder every day.
Remember that most serious assaults occur against people that know each other. In today's society that often means gangs fighting each other. Stay out of their way in Belize you will likely be fine.
In Central and South America there is a problem with theft of property. You can't leave your property laying around - it will be gone. It is common in all areas to have bars on the window, and high fences. Dogs to deter people, but the best thing is to have someone there watching over the property.
I have not come across expat that lives in Belize (or Costa Rica) telling me that the crime is so bad. Certainly we have never felt unsafe night or day in Belize.