Yeah, I would assume that this would be acceptable if you showed them that you set the charger to 50amp during the commissioning process. But perhaps they might say "This isn't good enough, because you could change it later after I leave". But yeah, the Tesla wall charger can be programmed to run at 15a-60a.
This is a long post - skip it if you don't care about how you're going to charge this new car of yours
First, it will mostly depend on your AHJ - Authoritative Housing Jurisdiction - the local code inspector whether, as to whether it gets passed or not. You should call your town office and ask what they would require. But here are some notes on this comment and others that followed it.
If you want to do it by code, then Romex 6-3, 60 degree rated, which is only rated at a continuous load of 55 amps, should NOT pass inspection if used with a 60amp Tesla wall charger - despite the fact that you could override the amount of current that charger can draw. It can pull 60 amps, so you need it on wire and breaker that can sustain 60 amps. 14-50 outlet would be fine with 6-3 but not if you're going to hardwire a Tesla wall outlet with it. Do people do it? Yes. Is it safe if you make sure your charger isn't pulling more than 50 amps? It
should be, assuming you did everything else right. Is it up to code? Nope, not on a TWC. And I'm guessing there are plenty of setups that aren't up to code that are "safer" than bad installs that are up to code, but that's sort of beside the point.
To speak to the 6-2/6-3 lingo.... The six is the gauge of wire, the second number is the number of conductors. 6-2 is two conductors and a ground wire. 6-3 is three conductors and a ground (it has an extra wire for neutral). But since the TWC only wires up with 2 hots and a ground (no neutral), 6-2 would be technically possible (though in violation of code) and so would 6-3 because the neutral wire would just be hanging out, not connected to anything (but also not up to code). I do know some people that have used 6 gauge romex (or NM-B), and just chose not to inspect it (cuz it wouldn't pass). I didn't want to go that route because, well, I don't want my house to burn down (or family to perish), and if I do have an issue, I want don't want an insurance company to deny a claim because I didn't pull a permit. You will read others on here to tell you to always pull a permit, and this is why.
If you want to be compliant with code, you will need individual 6 awg THHN wire (90 degrees, which if you look at the chart, will see it can carry more amps than romex 60 degree) for the hots and I used 8awg for the ground (think you can use 10awg). And that will need to be in at least 3/4" metal conduit, if in a garage, or schedule 80 PVC because it must be protected from physical damage (for good reason!).
Doing it yourself is not for the faint of heart, and sort of silly if you live in NJ or anywhere that gives you a rebate to install chargers (though TWC doesn't qualify in NJ amazingly enough). I had already ordered the TWC when I ordered the car before I realized the rebate stuff. Also, I thought it was easier than it looked and have service disconnect to de-energize my entire panel, and because of those reasons, decided to do it myself. I was able to borrow a conduit bender, and I'm very handy (and a good thing I was). I had to replace an LB box (cut away without hurting the wires in side) with a junction box as part of the project. I also ended up swapping out the 60-amp breaker I bought on Amazon because it was non-UL-listed and was getting hot and tripping, despite my correctly torqueing down the lugs properly. The new breaker only gets "very warm" after extended charging.
And despite all this effort, I think I will still take the charger down to 40 amps to reduce the load/stress on the circuit. 48 just isn't necessary! So keep that in mind when considering your charging options.
I have my inspection scheduled for Tuesday and guess we'll see!