Your coverage during the 30 day period is, I believe, only for the same coverage as for your most extensive coverage carried on any other car under that same policy.
That would mean that if you had theft coverage by virtue of "other than collision" coverage, sometimes referred to as Option D (this depends what state and what policy you have, of course) that same coverage may extend to your new car for 30 days.
But, if you do not have "other than collision" or Coverage D, which includes theft, you may be without coverage and that's what may have happened here.
In all cases, the coverage you have is what your policy says. To be covered for theft, you must carry theft insurance.
And remember: there may be no hard rules from one state to another.
More uniform rules will have to await the President's new mandatory national auto insurance policy legislation. That legislation will, of course, contain an extra wealth tax on those elitists who choose all the lavish frivolity that goes with owning foreign sports cars.