Kotlin provides seamless interoperability with Java, without compromising its own null-safety... almost. One exception is that Kotlin assumes that all types that are defined in Java are not-null.
To understand, let's look at JsonNode.get()
Platform types
public JsonNode get(String fieldName) { return null; }
Note that JsonNode is defined in Java, and is therefore a platform type - and Kotlin does not 'translate' it to JsonNode?, even though that would be technically correct (because in Java all types are nullable).
When calling Java from Kotlin, for convenience it's assumed that platform types are non-nullable. If this wasn't the case, you would always have to check that any instance of any platform type is not null.
So, to answer your question about what a 'platform type' is, it's a term that means
- some type that is defined in an external target language,
- you can't mention it explicitly in Kotlin code (but there's probably a synonymous Kotlin equivalent),
- and we're going to assume that it's non-nullable for convenience.
- Also the notation is
<type>!, for example String! - which we can take to mean String or String?
Nullability annotations
The closest Java equivalent of Kotlin's nullable ? symbol are nullability annotations, which the Kotlin compiler can parse and take into account. However, none are used on JsonNode methods. And so Kotlin will quite happily assume that node.get("") will return JsonNode, not JsonNode?.
As you noted, there are none defined for HashMap.get(...).
So how does Kotlin know that map.get("a") returns a nullable type?
Type inference
Type inference can't help. The (Java) method signature
public V get(Object key) {
//...
}
indicates that a HashMap<String, String> should return String, not String?. Something else must be going on...
Mapped types
For most Java types, Kotlin will just use the definition as provided. But for some, Kotlin decides to treat them specially, and completely replace the Java definition with its own version.
You can see the list of mapped types in the docs. And while HashMap isn't in there, Map is. And so, when we're writing Kotlin code, HashMap doesn't inherit from java.util.Map - because it's mapped to kotlin.collections.Map
Aside: in fact if you try and use java.util.Map you'll get a warning 
So if we look at the code for the get function that kotlin.collections.Map defines, we can see that it returns a nullable value type
/**
* Returns the value corresponding to the given [key], or `null` if such a key is not present in the map.
*/
public operator fun get(key: K): V?
And so the Kotlin compiler can look at HashMap.get(...) and deduce that, because it's implementing kotlin.collections.Map.get(...), the returned value must be a nullable value, which in our case is String?.
Workaround: External annotations
For whatever reason, Jackson doesn't use the nullability annotations that would solve this problem. Fortunately IntelliJ provides a workaround that, while not as strict, will provide helpful warnings: external annotations.
Once I follow the instructions...
Alt+Enter → 'Annotate method...'

Select 'Nullable' annotation

Save annotations.xml
Now node.get("") will show an warning.

This annotation isn't visible to the Kotlin compiler, so it can only be a warning - not a compilation error.