So here's how I look at it.
If ramped, the pilot flying the plane will be held responsible for flying in violation of the rules. Most likely, you will be asked if you knew about the discrepancy - if you say yes, you've acted willfully in violation of the rules, but if you say no they you will receive a violation for not conducting a proper preflight. There simply is no win in that situation. Even if you don't get asked whether you knew, the violation will be hung on you and it'll be up to you tp prove otherwise. I personally don't like to be put in a potential lose-lose situation. Other people have a different opinion, that's their choice.
In theory, the FAA could ask the FBO for all the names of renters when planes were out of compliance and hit them all with a violation. That applies for registration, W&B, pitot-static, and otherwise. A few days out and it probably won't be an issue (unless the FAA has a bee in their bonnet for that FBO), but longer term it will be. Not likely that the FAA will do this, but possible. They have gone after all students who used certain DEs for example.
Most likely, things that you can't detect (a pencil-whipped annual, for example) are not likely to fall on individuals. But things that are easily detected might.
I know most will think that the FAA won't do that, but the possibility exists and I've seen other agencies take similar steps. YMMV. And putting aside the FAA, it would also raise potential liability issues if there were a crash - if you knew of operations outside of the FAA rules you might well be roped into the case. Again YMMV. Different folks have different tolerances for risk.
Kudos for asking the question. If it were me, I'd find another FBO (I bought my plane during IFR training because of maintenance issues - broken stuff - that left the planes OK for VFR training but not for IFR flight). If you're still using an instructor there, you might also mention your concerns to him as his ticket is on the line, too.