Your inclinations seem correct to me, but I find if very challenging to be definitive without seeing images. 

There *are* use cases where branding adapts - off the top of my head Apple comes to mind. It's either just the name, the name and the apple, or just the apple. The apple icon can have gradients and a "shine" or be a flat singular color. For video, Apple just used the top of the apple icon, not even the entire icon. All this could also refer to MicroSoft and how they adapt their branding. Or FedEx, with its multiple color variations based upon service. (Granted these are well established brands which offers some freedom.)

Multiple variations are not *automatically* a bad thing... it's more about *how different* the variations are and what *specific* aspects are changing. If the core imagery is conveyed in relatively the same manner, there may be no harm in variations. The key to brand usage is *consistency*. If variations can be implemented but remain overall consistent with each other, there's no harm. (Again Apple, MicroSoft, and FedEx come to mind - wide variations, but consistent overall shapes.)

The possible technical, reproduction, issues regarding a blur seem irrelevant. The *conceptual* usage of a blur is what I would question. A blur, in itself, *seems* counterintuitive to a "logo". But again, without knowing the company or seeing imagery it's hard to be definitive. A "blur" for branding, to me, conveys a company with a lack of focus which is rarely a *favorable* impression. There's a **reason** one would find it difficult, if not impossible, to find a well-established company that uses any blur in their overall brand imagery.

I can't imagine how a "blur" is conveyed for something like a single color product brand placement (like a pen or keychain). And if it's conveyed well at such a small size, my inclination would be to use *that* variation for *all* usage. I, personally, am not of a mind to make a brand *more* visually complicated for some specific usage merely because it's possible. If a variation works well for silkscreening two colors on a t-shirt, then that variation should be used everywhere, as opposed to making the brand imagery more complex or detailed merely for web usage. Just because something *can* be done, doesn't necessarily mean it *must* be done.


And be aware "small thin lines" may **not** hold up at small sizes, which *may* negate the reasoning for creating such a variation. All lines "at size" will need to be **no smaller than 0.25pt** in stroke weight to ensure they are retained for *most* processes.

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**Form v. Function.** Branding actually has an imperative *function*. It is often too easy to get wrapped up in the form and lose sight of the necessary function.

What *may* be helpful is *how* different variations are *reviewed*. All proposed designs should be viewed in 1 color (or greyscale) and 1" at its longest dimension. And viewed at arms length or farther. **Often** merely doing this can *immediately* eliminate proposed designs. If a logo doesn't hold up when looking at it this way.... it's not going to do the job it needs to do, even if it is stunningly beautiful full size on a web site.