We would not expect the two methods to lead to similar answers -- we would expect the apparent rate of usage of Tide to be higher when the interviewers just asked whether the person used Tide than when they actually requested to see the box of Tide in the laundry room. Asking people whether they use a product is likely to lead to response bias -- if you just say "Hello, ma'am or sir, do you use blah?" people will tend to say yes even if they don't use blah, because people have a natural tendency to try to accommodate or please someone else and the pleasing answer to the question above is yes. Asking permission to go into the laundry room to see what brand of detergent is being used is likely to lead to a very high nonresponse rate, which opens the way to large biases of its own.
There are two main problems here -- the panel of Nielsen families was seldom changed, and the Nielsen people presumed that people were watching TV just because the set was on. If you choose a representative sample of the country (as far as TV-watching habits is concerned) in 1985 and try to use their viewing habits in 1994 as a good guess for what the rest of the country is watching that year, you run the risk of missing changes over time in who is watching TV (for example, if more and more young people are watching over time you will miss that because all of your 1985 people are getting older). The other problem is a kind of measurement issue -- just because the TV is on doesn't mean that anybody is watching it. Maybe people would be ashamed at how lowbrow their viewing habits are and leave the TV on PBS when nobody wanted to watch anything else.