OP - I go with the way you interpret the text.
From the FAQ
Now the assumption is for any magic item that the caster level is the minimum required to cast the spell - in this case the default would a 3rd level caster.
It is possible to create a ring of invisibility with a higher caster level, but the cost would go up accordingly.
As far as justifying the 20,000 gp cost - well, the DMG talks about "adjusting" prices based on actual worth (pg 282) and look at the prices of the rings in general, especially around the same cost as the ring of invisibility - seems pretty reasonable for a relative "actual value" to me.
From the FAQ
What is the duration of the invisibility granted by a ring
of invisibility?
In general, you should assume that any spell effect
mimicked by a magic item treats all variables of the effect as if
it were the spell cast with the item’s caster level. In this case,
the duration of the ring’s ability is the equivalent of an
invisibility spell cast by a 3rd-level caster (the ring’s caster
level): 3 minutes. Of course, nothing prevents a character from
activating the ring’s power more frequently than this (thus
ensuring a constant invisibility), as long as he’s willing (and
able) to spend the actions to do so.
Now the assumption is for any magic item that the caster level is the minimum required to cast the spell - in this case the default would a 3rd level caster.
It is possible to create a ring of invisibility with a higher caster level, but the cost would go up accordingly.
As far as justifying the 20,000 gp cost - well, the DMG talks about "adjusting" prices based on actual worth (pg 282) and look at the prices of the rings in general, especially around the same cost as the ring of invisibility - seems pretty reasonable for a relative "actual value" to me.