Distributed data analytics platforms (i.e., Apache Spark, Hadoop) provide high-level APIs to programmatically write analytics tasks that are run distributedly in multiple computing nodes. The design of these frameworks was primarily motivated by performance and usability. Thus, the security takes a back seat. Consequently, they do not inherently support fine-grained access control or offer any plugin mechanism to enable it, making them risky to be used in multi-tier organizational settings. There have been attempts to build "add-on" solutions to enable fine-grained access control for distributed data analytics platforms. In this paper, first, we show that straightforward enforcement of ``add-on'' access control is insecure under adversarial code execution. Specifically, we show that an attacker can abuse platform-provided APIs to evade access controls without leaving any traces. Second, we designed a two-layered (i.e., proactive and reactive) defense system to protect against API abuses. On submission of a user code, our proactive security layer statically screens it to find potential attack signatures prior to its execution. The reactive security layer employs code instrumentation-based runtime checks and sandboxed execution to throttle any exploits at runtime. Next, we propose a new fine-grained access control framework with an enhanced policy language that supports map and filter primitives. Finally, we build a system named SecureDL with our new access control framework and defense system on top of Apache Spark, which ensures secure access control policy enforcement under adversaries capable of executing code. To the best of our knowledge, this is the first fine-grained attribute-based access control framework for distributed data analytics platforms that is secure against platform API abuse attacks. Performance evaluation showed that the overhead due to added security is low.