Statistic count not working with API call
Node views are only counted when node_view() is invoked (i.e. when the node is actually viewed).

When retrieving a node via services you're not, conceptually, "viewing" it, so you shouldn't expect the view count to increase.

In order to get your desired workflow, you'll probably need to implement a custom services resource which updates the statistics manually when a node object is requested. See How to create a custom resource with Services-3.x for more info.