Heh, not knowing Java very well, I scoured the BigInteger docs for quirks and loopholes, then gave up and found your comment. I guess "java.security.SecureRandom" sounded too impregnably secure to be worth looking into.
Java Service Providers (SPI) trigger before main() is run. You can create a SecureRandom() provider, add it to the classpath with SPI, removing other providers.