VR-HDB
Nope "Available" and "open" are not quite the same.
An adequate airport must be available with all services etc but can be closed due weather, therefore it is not "Open"
A Suitable airport has all the same requirements as an "Adequate" airport but includes the requirement to be open with specific weather requirements.
Plainsoul
The documents referred to by Mutt for Boeing and FAA are "ADVISORY" Airlines take these and adopt either in part or whole the procedures (If subject to FAR's) and then have these procedures ratified by their applicable regulatory authority.
I'm not 100% with JAR but they are similar but not the same.
Depending on which set of rules your company adopted and had certified you are most probably correct, in your beliefs.
The intent is that you shall not enter an ETOPS segment unless you have a "SUITABLE" Airport with weather minima as specified in your ETOPS specs, this may or may not be the same as at fligh planning, but generally is the same as that required for an enroute alternate, if at least one suitable airport is not available within your particular ETOPS flight time limit then you cannot enter.
However if after you enter it goes down or closes it becomes a "Captains decision".
This is basically what Boeing and the FAA reccomend but as I said they are "Advisory" documents that must be adopted.
Hope this helps.