Although ground rims and mouths are not common on Italian glass, I would not look away from Italian too quickly based on that. Many of the bud type and teardrop stle vases by Italian houses have ground mouths due to the extreme difficulty to create a very small opening in a non ground piece. I also have at least one piece which I am fairly sure is a Cenedese ashtray with a ground upper rim, and it is not small at all. In commenting on the other piece I posted in a similar shape, Marcus did note that at one time he had a similar piece with a Galliano Ferro label
I also saw a vase in similar colors to my vase on ebay, no fins, but the Galliano Ferro label and a ground mouth.
Additionally, there is a teardrop Cenedese vase with a label on ebay right now that has a ground mouth and flat ground and polished base....
I would have to say that my observation would be that many of the small mouthed teardrop style pieces have ground rims..... It is far less common with other Italian pieces....
Craig