Right. The issue comes up if you're circumventing fare rules like minimum stay or Saturday night stay. Typically the business traveler who has to be in the same city, say Monday-Friday of two consecutive weeks, would have the most to gain from nesting. I have still never heard of a case when the airline has enforced this, but it is against the rules to nest tickets in a way that violates the fare conditions.

By definition, if the two itineraries are on separate airlines, then you are not violating any fare rules. It might be overkill to also credit to two different frequent flier programs, but that would provide total safety.

Though this is completely irrelevant to the OP's question, I have to ask: why would you have multiple rental cars at the same time? I guess if you got a weekly rate, but needed to take a day-trip to a location (e.g., outside the country) that was not allowed by that rate, then it might make sense to rent a second car. Do car rental companies prevent you from having more than one car out at the same time? (Assuming that you are the only driver on the reservations.)