It certainly sounds like you got a visa exemption at the border. 30 days. Perhaps the officer did not see your 60 day tourist visa. Good luck but best you get back to immigration immediately.
800,000 thai baht, in a thai bank account 3 months before application and 3 months after your visa. All the required documentation is easy to find online.
I tried to do an extension on my visa exemption a few years back. It got absolutely ridiculous. They wanted receipts for 30 days, but like your friend I was travelling around. It became so stupid that I just got on a bus and went to Cambodia and got a thai visa there. From my experience I always advise getting a visa prior to arrival, making life much easier. I hope your friend gets it sorted.
I usually fly to udon thani then take minivan to the border. Once over the border take the local bus to central Vientiane. Be warned...you must prebook an appointment at the Vientiane office. There are no walk ins. Best to book 2 weeks or more before you go there as slots are limited. Good luck.