Is it possible to accidentally use some paid feature in Oracle XE database while in an Enterprise environment?
Oracle Express Edition is free software that can be used even for commercial purpose.

What the DBA said is true for Enterprise Edition where some features can not be completely disabled (e.g. Advanced Compression), and it was true for Standard Edition in versions below 11g (e.g. Diagnostic Pack).

Express Edition will be fine.

For a personal learning/development environment, you could even use Enterprise Edition, if you will be the only one using it.