I do believe that this is where the term "Smyth Lens" very probably originated. Indeed, the first time I ran into the term was in reading Harry Rutten and Martin van Venrooij's book TELESCOPE OPTICS (c. 1988 Willmann-Bell). On page 175 of the 1993 edition, the authors state:

"As mentioned above, it is possible to reduce astigmatism in a positive eyepiece system at the expense of introducing field curvature. By placing a negative lens between the objective and the positive eyepiece, however, we can compensate this field curvature. The reason is that the negative lens introduces curvature in the intermediate focal surface F2. If this is chosen to match that of the positive lens, the resulting combination of lenses can be free of both astigmatism and field curvature in the imaginary focal surface F2.

The design principle of the Nagler is not totally new. The combination was proposed long ago by Smyth; hence, the negative lens is called a Smyth lens (see ref. 16.1)."

Now some eyepiece manufacturers just slap in a negative lens in front of a simpler eyepiece design to try and make it work a little better at what amounts to a longer focal ratio. This would be a "built-in" Barlow. The Smyth lens, however, would be specifically designed so as to compensate as much as possible for extensive field curvature produced by the positive lens set that has already dealt with the astigmatism problem. There are a few eyepieces where the Smyth lens also serves as a sort of Barlow (the 5-8mm Speers Waler eyepiece for example). However, the overall design and intent of the negative field flattener is for field flattening and not just to bump up the f/ratio to a point where a simpler eyepiece can handle the narrower light cone. Clear skies to you.