The answer to your hypothetical question is yes, two llc's can have the same owners while only one is liable in a given situation. That's the whole point of setting up an llc, to protect its owners and their other assets (i.e. the second llc) from liabilities which the llc might incur.
The advice you've been given attempts to guard against the possibility of piercing the corporate veil, and doesn't really address direct liability of each llc.
In the particular situation you have posited, even assuming there is no piercing of the corporate veil (which depends on, among other things, whether the owners exercise the proper formalities in operating the llc, and in keeping its affairs and assets separate and independent of the owner's own, and of the assets and affairs of the other llc) it would be difficult. First in the scenario you posit, llc 1, the party which signed the contract, is in at least as much danger as llc 2, which only acted as an agent of llc 1. The claim would bethat Llc 1 breached the contract by failing to provide safe repair work (even if a non-party to the contract was hurt, he/she would sue the homeowner who would then sue llc 1), although llc 2 could also be independently liable for negligence. Also llc 2 would be liable to llc 1 for breaching its contract with llc 1. If a customer got a judgment against llc 1 which llc 1 could not satisfy, the customer could theoretically take over llc 1's assets, which would include llc 1's claim against llc 2.
I'm sure there are many creative ways to avoid or minimize the issue, and you may want to consult a Florida attorney about it. One thing I would advise though is to have the llc which signs the contract do the work. The other can simply provide administrative services, like accounting, billing, etc., for a fee. In this sutuation, there would be no basis apart from a claim to pierce the corporate veil) to hold llc 1 liabile for any accident (be aware, thought, that if you try to shield llc 2's money by having it pay llc 1 an improperly large fee for the administrative services, it will be evidence that can be used to pierce the corporAte veil). This may not solve all your issues, but it's a good start.
Another guardrail would be to have a limitation of liability provision in the contact the customer signs, for example limiting liability to a refund of the monies paid by the customer, and not to include consequential damages. Such provisions are not enforceable in all situations, and won't help you against a suit by a non-party to the contract, but it can't hurt and presents another obstacle to a claim....
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