They shouldn't have. It was totally fine of them to do this.
Why?
Because when a famous singer dies, people want to download their songs.
Microsoft wasn't using her death to try to gin up demand, it was trying to satisfy existing demand.
If you like Amy Winehouse and are sad that she's dead and want to buy her music that you don't already own, there's nothing inappropriate about that.
While the Microsoft controversy was going on, Winehouse was topping the iTunes charts. Which means people -- her fans -- wanted to download her songs. And there are services that help you do that! And it makes life more convenient for them to know about these services and use them!
After Michael Jackson's death, the concert documentary movie This Is It became the highest grossing such movie ever. Why? Because people were sad that Michael Jackson was dead, and they wanted to see a movie about him. And there is nothing wrong with that!
Now, obviously there are tacky ways to promote these things. (And the tweet wasn't particularly tacky.) But our entire modern civilization is based on the idea that people satisfy other people's demand for goods and services in exchange for money. And a tweet is a tweet.
Imagine the reverse: imagine that whenever a musician died, all the record stores, from Virgin to iTunes to Zune, stopped selling any music or any merchandise related to that musician for an appropriate (how long?) mourning period. Not only would this make no sense, fans would be furious! Because it's fans who want to buy that music and that merchandise.