Agreed. Also, there are two very different sets of federal laws in play, unrelated to state law.
- Overtime is a function of hours worked in the work week and is controlled by a federal law called FLSA. While FLSA is pretty much Exceptions-R-Us, I am not familar with any FLSA exception related to employer provided housing. Now employer provided housing (called "facilities" in FLSA) may possibly count towards the FLSA minimum wage requirement, but as far as I know, not the overtime requirement.
- Unrelated to FLSA, there is a very seperate law called IRC (Internal Revenue Code). That law says that EVERYTHING provided to the employee as a result of the employment relationship is fully taxable wages to the employee UNLESS the employer can hard support one of the very few exceptions. The obvious housing related exceptions are job-requirement or product-discount. An example of the first is a lighthouse keeper, who could not do his/her job unless they lived in the lighthouse. An example of the second is a maintence person at an apartment building who is not legally required to live there (hard to get by IRS), but who can legally be discounted something like 20%.

IMO, the implied linkage in the orignial post between paid overtime and employer provided housing is not obvious.