Theft is the taking of property with intent to permanently deprive. This matter being discussed is a civil issue and no law enforcement officer is going to get involved.
Let's see what Black's Law Dictionary has to say:
Theft
n. the generic term for all crimes in which a person intentionally and fraudulently takes personal property of another without permission or consent and with the intent to convert it to the taker's use (including potential sale). In many states, if the value of the property taken is low (for example, less than $500) the crime is "petty theft," but it is "grand theft" for larger amounts, designated misdemeanor or felony, respectively. Theft is synonymous with "larceny." Although robbery (taking by force), burglary (taken by entering unlawfully) and embezzlement (stealing from an employer) are all commonly thought of as theft, they are distinguished by the means and methods used and are separately designated as those types of crimes in criminal charges and statutory punishments.
Taking
In criminal law and torts. The act of laying hold upon an article, with or without removing the same.
Outside of mechanic's liens, the actions of the mechanic in this case are not supported by any law of which I am aware. I am only aware of the laws of California. If a work contract contained that clause which Tom mentions I, as customer, would either strike the clause as agreeable to the shop or take my biz elsewhere.
As what Ron says WRT to what the FAA says WRT this instance, they are a regulatory agency of which does not have jurisdiction over how business in conducted, ie, contract law.
In either case (what Tom or Ron say), it could be that those are allowable as far as influencing the courts, but they only muddle the waters and are not likely to prevail over state tort law.
Also, as it has been shown repeatedly, and likely proven in case law, that the absence of logs detracts a significant value from an aircraft, and that the aircraft is valued at least tens of thousands of $$, this rises to criminal behavior as defined by Black's.
That ol boy, the A&P, better get on the stick and find a more amenable way to settle the disagreement.