(Couldn't find explicit RAW to support this)
You are correct in stating that 'the ability does not inherit rules from any other form-changing abilities', nor is it labeled as similar to any.
However, comparing the other common shape change rules, you see the following (all emphasis mine):
Alternate-Form and Change Shape Monster Abilities
Any gear worn or carried by the creature that can’t be worn or carried in its new form instead falls to the ground in its space. If the creature changes size, any gear it wears or carries that can be worn or carried in its new form changes size to match the new size. (Nonhumanoid-shaped creatures can’t wear armor designed for humanoid-shaped creatures, and viceversa.) Gear returns to normal size if dropped.
This is clearly different than the Shapeshift class feature. Note that there's no "melding gear" effect here.
Standard Druid's Wild Shape
Any gear worn or carried by the druid melds into the new form and becomes nonfunctional. When the druid reverts to her true form, any objects previously melded into the new form reappear in the same location on her body that they previously occupied and are once again functional. Any new items worn in the assumed form fall off and land at the druid's feet.
This is in essence the same behavior as the Shapeshift variant, with the added explicit statement that gear obtained in the 'non-true' form falls off when you revert to your true form.
Transformation Spells such as Alter-Self, Polymorph and Shapechange
When the change occurs, your equipment, if any, either remains worn or held by the new form (if it is capable of wearing or holding the item), or melds into the new form and becomes nonfunctional. When you revert to your true form, any objects previously melded into the new form reappear in the same location on your body they previously occupied and are once again functional. Any new items you wore in the assumed form and can’t wear in your normal form fall off and land at your feet; any that you could wear in either form or carry in a body part common to both forms at the time of reversion are still held in the same way. Any part of the body or piece of equipment that is separated from the whole reverts to its true form.
Right, so again we see the "melding gear" effect, and again, it applies only to gear carried in the true form - anything gained in an alternate form falls off when you revert (unless you can wear or hold it in the same way in both forms).
From these examples I see two possible interpretations (which one you use basically boils down to your GM's call and your group play style):
The "Power Gamer" Interpretation
Other mentions of the 'melding gear' effect explicitly state it applies only to the true form, while this is absent from the Shapechange variant. By taking this omission as intentional, you can conclude this effect works on any form - effectively allowing your druid to have a different inventory for each shape.
Moreover, you may claim that the Shapechange variant druid doesn't really have a true form, as he can stay indefinitely in any of his forms...
This interpretation makes this feature much stronger, and will allow for less cumbersome gameplay if you intend to use magic items to buff each form (as your druid won't have to worry about donning armor and wearing amulets, belts and rings every time he changes - as well as where to carry them the rest of the time...).
However, it can easily be abused, turning your druid to the party's pack-mule / walking bag of holding...
The "If it Quacks like a Duck" Interpretation
There seems to be two different themes for shape-changes in 3.5E - one without the 'melding gear' effect (which applies mostly to monsters), and another with it - which applies mostly to PCs and NPCs. All other descriptions of this effect always make a clear distinction between the 'true form' and alternate ones, and apply the effect only for transformations from the true form. It seems more balanced to apply the same treatment for the druid variant too - especially as this feature's description does use the term 'true form', hinting that regardless of how much time he actually spends in that form, the druid still have one.
This option is less powerful, but has less impact on game balance. It may force your druid to invest in wild-armor which changes shape with him, and perhaps have some of his alternate form's gear carried by other party members.
Either way, I'd ask the GM to allow for items relevant for both shapes (such as magic amulets or belts) to remain 'unmelded' and functional across shapes, so you don't need to have several copies of each (for option 1), or depend on an ally to dress you up before and after every change (for option 2) - of course, they may cost more than standard magic items for this additional ability...