I don't think I'm unique for putting miscellaneous stuff like this on a credit card, and not even necessarily the one my bank offers. Not to hide the transaction, but because charging to debit/checking would make tracking my monthly expenses less straightforward. Payments online are also safer on credit in case a chargeback is required.
Also, are you sure you don't mean "proof of employment" showing the last three months of direct deposits? I've never heard of anyone asking for any other transactions. Similarly, pretty sure loan applications are based on credit reports. Transactions aren't relevant unless they got flagged for something so bad they showed up in the credit report (fraud, missed/late payments, etc).
Ive never been hit by something like this but I have friends who have:
https://www.reddit.com/r/personalfinance/comments/12s8257/la...
(Maybe this is just the horrendous Australian market talking).
If they're too cheap to pay for a basic background check, there's no telling what kind of shady people will be your neighbors or how unmaintained those apartments are. Just find somewhere else or provide the bare minimum that will convince them (checking account only). Clearly they have no way to find what else you have, and nobody else is taking this that literally.
