Yes, the right to private use is covered by the Swiss Copyright Act, Art. 19 Para. 1 a of which reads:
“Published works may be used for individual purposes. Individual purposes shall mean: any use of a work in the personal sphere or within a circle of persons closely connected to each other such as relations or friends”.
Yes, according to the limitation in the Swiss Copyright Act, the internal use of works is permitted, even if the author has assigned the online rights to the publisher or granted it an exclusive licence. However, there are restrictions set out in the Act which must be complied with:
Art. 19 Paras. 1 c and 3 of the Copyright Act:
It should be noted that if a publishing contract is concluded with a foreign publisher, the wording of this contract may mean that foreign law will apply, and most states do not permit a comparable internal use.
Internal use is subject to a fee which is paid to the copyright holder (Art. 20 Para. 2, Copyright Act). If the right is assigned to the publisher, the latter becomes the copyright holder. The claims to payment can only be asserted by a licensed collecting society (Art. 20 Para. 4, Copyright Act), in Switzerland, for instance, by Pro Litteris. The deposited full text (pdf) must have been acquired lawfully. Entire books available commercially or copies thereof cannot be made accessible internally, nor can individual articles from journals available commercially (e.g. via the publisher’s website).
If this serves to secure and maintain its stocks, i.e. if it concerns works and articles that the library has or had licensed, this is permissible:
Art. 24 Para. 1bis of the Copyright Act: “Publicly accessible libraries, educational institutions, museums and archives can make the copies necessary for backing-up and preserving their stocks provided that these copies do not pursue economic or commercial purposes.”