While you may be correct in certain circumstances, your wording gives a false impression that this always works. You must disclose the best mode when filing a patent application.
The specification . . . shall set forth the best mode contemplated by the inventor of carrying out his invention.
"The best mode requirement creates a statutory bargained-for-exchange by which a patentee obtains the right to exclude others from practicing the claimed invention for a certain time period, and the public receives knowledge of the preferred embodiments for practicing the claimed invention." Eli Lilly & Co. v. Barr Laboratories Inc., 251 F.3d 955, 963, 58 USPQ2d 1865, 1874 (Fed. Cir. 2001).
The best mode requirement is a safeguard against the desire on the part of some people to obtain patent protection without making a full disclosure as required by the statute. The requirement does not permit inventors to disclose only what they know to be their second-best embodiment, while retaining the best for themselves. In re Nelson, 280 F.2d 172, 126 USPQ 242 (CCPA 1960).
As you hint at, there's nothing wrong with combining one invention with another, one protected by patent law and the other by trade secret.