The reason why Americans do not believe this is not because they despise Merkel. The reason why Americans do not believe this is simple: They are used to it in the US. It is completely normal in the US

Besides the strange and unsubstantiated reasoning you just gave as to why Americans think there are slums in Germany, there's another possibility - reading. Here's a clip from an article from Spiegel:

Misery is moving house in Berlin: Many of the city's problems are shifting out toward the city limits, into new slums which are starting to resemble Paris's dreaded banlieues. Meanwhile, areas such as northern Neukölln, neighboring Kreuzberg and other parts of the city traditionally populated by workers and immigrants are becoming increasingly popular with middle class residents and hipsters. Tourists are also attracted to the areas by glowing articles in the international media.

Those who, like Kira's parents, can no longer afford the rents in the city center, withdraw to the concrete ring that encircles the German capital. Of Berlin's 3.45 million residents, 420,000 live in these high-rise housing projects on the city's outskirts, in neighborhoods that have so far attracted little media attention.

"The slums of the 21st century are threatening to form on Berlin's outskirts," warns sociologist Hartmut Häussermann. Teenage gangs fight over territory on the streets and squares, sometimes attacking unlucky passersby without warning. Three weeks ago, in an incident that shocked Germany, four young men attacked a painter who was passing through the Lichtenberg subway station on his way home, beating him into a coma for no apparent reason.