I looked at this a few days ago when you put it on and decided to give it a little thought before answering.
At this point in time I am not aware of a lid like yours that I can attribute to S&W.
However, I suppose we have to go through this a little.
On the one hand you say that the colour is not true to the base and that the lid is not a good fit. Quite obviously there are also no bubbles in the lid, so one might well assume that it did not start life as the lid to this bowl.
Conversely, depending on the thickness of the glass, whether or not it was made at the same time as the base, etc., it is still possible that it could be a S&W lid. Equally, have you ever tried to match a lid and a base (or a stopper with a decanter base for that matter)? It is a very difficult thing to achieve and requires a modicum of luck, especially if you are to even approximate a colour match as well (clear being somewhat easier). The lids on the ginger jars are not a particularly good fit, so that also makes one wonder. The biggest problem is the lack of bubbles, which certainly leaves a huge question mark about whether or not the two pieces are original to each other.
Not really an answer I know. More of an analysis of the characteristics which allows one to make a judgement - which I'm sure will divide into two clear lines of support. My guess
is that they could have been bought at the same time as each as a sort of mix and match that appealed to the owner at the time, but without anything to back it up, other than the problem of matching the top and the bottom at a later date.
You pays ya money and ya takes ya choice