Well, the company has to be real and they can presumably check that on various online databases based in the country the company is registered in. If it checks out, then the letter presented is likely to be legit too.
I was told by Vientiane the money needs to be banked for 3 months. Savannakhet is possibly 6 months; not quite sure. In any case, they're quite strict and best to use Taipei instead.
In a sense, it remains a grey area, but the Thai authorities have finally decided - you don't need a work permit to work remotely and they've created a visa called the DTV to allow remote work.
However, if you're only coming to Thailand for 2 weeks and wish to work remotely, then you can and don't need to go through the rigamorale of applying for a DTV as your stay is too short to make it worthwhile.
That is, unless you wish to come and go frequently, then it might be worth it.
However, for an actual "digital nomad" who is jumping between countries and doing a little bit of remote work in between, that's fine to do on a visa exempt or tourist entry as you'll be moving on to the next country afterwards anyway and have no intention of residing in Thailand.
The DTV was basically designed, in part, to provide a pathway for longer term residence to remote workers.
I filled one out just a few weeks ago coming in by land from Cambodia. However, it's not so bad at land borders (unless you're at a busy one) because chances are you'll be the only person there, needing to fill one out (and indeed, I was). Apart from my family and I, no one else was crossing the border at the time I was and Thais have not been required to fill out the form since 2017.