This is not true. The elevated risk of AIN is special to Methicillin (no longer in use precisely for this reason), not anti-staphylococcal penicillins as a group.
AMBOSS lists AIN as an adverse effect of all the beta-lactams, noting only methicillin as especially associated with it (https://next.amboss.com/us/article/mm0VTg#Y6b3413c96a064eefa8f8fee0b1104adb). Under AIN, AMBOSS lists a variety of drug classes as causes without specifying any group (https://next.amboss.com/us/article/Jg0sw2?q=acute%20interstitial%20nephritis#FTcgsb0). The source which AMBOSS cites for their AIN page states that Amoxicillin and Ciprofloxacin are the antibiotics associated most with AIN in todays practice.
I think this question should either be removed, or replaced with something more along the lines of "Historically, which modified penicillin antibiotic (rather than group) was especially associated with AIN?"
Real-life and boards can be different and that's okay. sticking to FA24 (see comments)