I agree with you. It could work, and that's what I answered the OP, but personally I would not risk it. A week is really short, I would allow for at least a good month seasoning before applying.
Good point, but I guess it's easy to modify the date and time of the timestamp by setting one's phone to another date and time. Not a very safe way to conduct a check on the applicants' location.
Participant(e) anonyme Where did you apply BTW? If their request for further documents mentioned specifically "a letter stating that you can work remotely", then I guess you should be fine if your letter says something along the lines of "work remotely from anywhere in the world". If it mentioned specifically "a letter stating that you can work remotely from Thailand", then don't risk it, get a letter mentioning Thailand.
Participant(e) anonyme Yes, way to go. Does not look bad at all.
If you can figure out anything else you could show to them, enclose it. Maybe proof of finances that do not qualify for the 500K THB (brokerage account, etc.).
They could have sent a standard description. Write a cover letter in which you explain what you've just explained in your post. Send the pay slip you already have. Try to think of something you might have, to show on top of that. You haven't sent the extra letter written by the CEO of your company yet, have you?