Okay, I think it is important to make a difference between SEPA and the term “IBAN/BIC” transfer here. Because the IBAN/BIC based infrastructure can be used for other currencies as well. As I understand it, this is for example necessary to set up direct debits and card payments.
Both cross boarder direct debit and card payments based on IBAN/BIC are an important part of the SEPA idea where direct debits are possible between different currencies all over the SEPA countries that don’t have EUR as the local currency. If one sets up a direct debit there, the payment will be exchanged by the payers bank, not by the payees bank. And as far as I understand it, the banks can’t charge you more for a cross-border transaction than for a national transaction unless there is currency exchange involved. (They can charge separately for currency exchange.)
And the Wikipedia article clearly states that the regulation was limited to EUR transfers but was changed in 2009 to cover all currencies. Wikipedia might be wrong, of course.
Since 2009 the European Union Regulation No 924/2009  controls cross-border payments in the European Union. In the new regulation Article 1 (q.v., Ref.4) states that an IBAN/BIC transfer within Single Euro Payments Area (SEPA) must not cost more than a national transfer, no matter which currency is used. The receiving bank can charge for exchanging to local currency.
Prior to this, in 2002 the European Union relegated the regulation of fees a bank may charge for payments in euro between EU member states down to the domestic level, resulting in very low or no fees for electronic transfers within the Eurozone. In 2005, Iceland, Liechtenstein, and Norway joined the EU regulation on electronic transfers. However, this regulation was superseded by the Single Euro Payments Area (SEPA), consisting of 32 European countries.