My impression from the literature is that physicists are still divided on this question. The Quantum Information Theory camp says the latter, but the Quantum Optics people say the former.
A related, but distinct, issue is whether one regards the concept of «open system» as a mere mathematical convenience, or as a fundamental concept. This issue has received less attention. It is striking that in Dirac's basic textbook, «system» means «closed system», just as it always did in Hamiltonian mechanics: there is no other kind of system. Obviously in order to do some practical calculations in physical situations where dissipation or decoherence plays a role, the device of an open system is convenient. The issue of whether it is fundamental is still not settled.
Both issues are related to one's sympathies or lack thereof with «decoherence» as the answer to the puzzle of quantum measurement. In spite of some claims to the contrary, decoherence is not yet accepted by consensus. See Stephen Adler's well argued paper pointing out the serious problems with decoherence when taken as the solution to the quantum measurement problem (everyone agrees that decoherence is sometimes a convenient mathematical device)
Why Decoherence has not Solved the Measurement Problem: A Response to P. W. Anderson. Stephen L. Adler. Stud. Hist. Philos. Sci. Part B 34 no. 1, pp. 135-142 (2003). doi:10.1016/S1355-2198(02)00086-2, arXiv:quant-ph/0112095.
See also my own (which sometimes, on a bad day, doesn't even convince me)
Thermodynamic Limits, Non-commutative Probability, and Quantum Entanglement. Joseph F. Johnson. In Proceedings of the 3rd International Symposium, Quantum Theory and Symmetries (Cincinnati, USA, 10-14 September 2003). arXiv:quant-ph/0507017
and the excellent paper by the great Roger Balian and two assistants,
The quantum measurement process in an exactly solvable model. Armen E. Allahverdyan, Roger Balian and Theo M. Nieuwenhuizen. AIP Conf. Proc. 750, pp. 26-34 (Foundations of probability and physics - 3, Vaxjo, Sweden, 7-12 June 2004). doi:10.1063/1.1874554 arXiv:cond-mat/0408316
all of which should be studied in order to make up your mind on the subject. Balian, as all statmech people, relies heavily on the use of the density matrix without enquiring too closely as to its foundational status. But since there is real important physics in their paper, it (and its precursor zipped files posted at http://www.chicuadro.es/ , H. Green, Nuovo Cimento 9 (1958), 880, written under Schroedinger's influence while at Dublin---but note that decades later, having long escaped Schroedinger's influence, Green adopted an opposing viewpoint) is of key importance to answering your question.