The BSD license does not grant any sublicensing rights. It clearly says that the notice and disclaimers must be preserved.
The original license required copyright notices in binary code. A newer form does not, but this is for pragmatic reasons. The binary code is still copyrighted. If you decompile it into a source language, then you probably have to restore the copyright notice and disclaimers.
When a proprietary, binary-only program with a highly restrictive EULA contains BSD code, those sections of the machine language which correspond to the BSD code are not actually under the EULA. They are not sublicensed, but only used with permission, as granted by the original license.
The original license required copyright notices in binary code. A newer form does not, but this is for pragmatic reasons. The binary code is still copyrighted. If you decompile it into a source language, then you probably have to restore the copyright notice and disclaimers.
When a proprietary, binary-only program with a highly restrictive EULA contains BSD code, those sections of the machine language which correspond to the BSD code are not actually under the EULA. They are not sublicensed, but only used with permission, as granted by the original license.