I have found on a few sites, one was even a site run by a law office on Koh Samui, the following:

...single entry tourist visas. These used to be valid for a stay of up to 60 days but from October 1 they are valid for a stay of 90 days. They cannot be extended.

Can anyone tell me if this is true under the new Visa rules?

It is not true.

I have found on a few sites, one was even a site run by a law office on Koh Samui, the following:

...single entry tourist visas. These used to be valid for a stay of up to 60 days but from October 1 they are valid for a stay of 90 days. They cannot be extended.

Can anyone tell me if this is true under the new Visa rules?

The visa is still valid for 30 days but you can go out of Thailand at the end of it and stay for a maximum of 90 days with any number of re-entries. Within a period of 6 months.

After that, you'll have to be out of Thailand for 90 days before being able to come back...

A tourist visa has nothing to do with visa free entry for 30 days allowed to about 41 countries. A tourist visa allows a stay of 60 days for most that can be extended another 30 days. For others, mostly visa on arrival countries, it allows a stay of 30 days that can be extended twice for another 30 days each.