Should not appropriate HTML files...

So Mac OS X automatically chose Textastic as the default and you didn't select it in the "Get Info" dialog in Finder?

It doesn't do that on my machines - Safari is still the default. I'd have to explicitly tell the OS to use Textastic "to open all documents like this one".

Is this on Mountain Lion?

Nope. I never selected it. Actually, I didn't notice this until I typed "open output.html" in a terminal window and it opened Textastic instead of Safari. I don't think I even edited an HTML file in Textastic yet.

And yes, this is in ML. Just reverted back to Safari in the Finder.

Textastic uses the value "Owner" for the "LSHandlerRank" key for HTML documents in its info.plist.

I assume that launch services randomly chooses one of the "Owner" apps for each file type to be the default app.

But, Safari has the key "LSIsAppleDefaultForType" set to true which should probably rank higher.

This is what the docs say:

LSHandlerRank: Determines how Launch Services ranks this app among the apps that declare themselves editors or viewers of files of this type. The possible values are: Owner (this app is the creator of files of this type), Alternate (this app is a secondary viewer of files of this type), None (this app must never be used to open files of this type, but it accepts drops of files of this type), Default (default; this app doesn’t accept drops of files of this type). Launch Services uses the value ofLSHandlerRank to determine the app to use to open files of this type. The order of precedence is: Owner, Alternate, None.

Since Textastic is a creator of html files, I chose "Owner" and not "Alternate".

I guess changing it to "Alternate" would leave Safari the default in all cases.