People might see and at some level be influenced by those headlines not because they are dumb, but just because they are there, and indeed given undue prominence on the BBC website. The viewer may not have the time to read the full story. I've noticed that news about rising house prices is generally given higher prominence (e.g. included on main news page and leading story on the business news page) whereas news about falling house prices is given lower prominence (e.g. no mention on main news page and tucked away at bottom of business news page).
And the headlines always provide a positive spin on the news (to those who subscibe to the view that rising house prices are a good thing). Why was the headline for this news "House prices increase by 0.4% in August" or similar - that is the real news.