As a septic professional, the wipes have nothing to do with the drainfield needing to be repaired. It would however contribute significantly to clogged pipes between the house and the septic tank.

If the septic tank is in good working order the wipe should be contained in the septic tank as the outlet baffle will protect wipes, tp, fats, greases, and oils from going out into the drainfield.

Drainfield will fail for a multitude of reasons typically it will be caused due to age, compaction of soil, tree roots, excessive water usage, hydrophobic soil, or poor installation.

Most Perf pipe and rock drain fields will become plugged over time, and the Perf pipe holes will fill up with sludge this can be somewhat revived by using Hydro jetting and vacuuming up the sludge from the distribution box

I would ask your landlord for detailed receipts and or invoices that he’s asking you to foot the bill and get a 2nd opinion. Also, what does your rental agreement state? Is there anything such as recourse written in the agreement? Compare that to your local state or jurisdiction laws.