I don't think the title of this thread is accurate. The link provided gives no indication whatsoever that IB is no longer interlining. Interline agreements apply to pax travelling on one ticket covering flights of two (or more) airlines. Strictly speaking they never covered the situation with two separate tickets, although some airlines checked through bags at least to connecting flights operated by themselves (and their alliance partners - sometimes).

All OW airlines, as well as many unaffiliated airlines, have explicitly stopped this practice not covered by the interline agreements and decided to stick to their wording. So IB is not an exception, but just followimg the rule.

On the same ticket, you can still check you luggage through (unless one of the other exception applies).