The idea of someone profiting from the trademark or patent of an idea because they 'thought of it first' may be abhorrent to you, but it's the way this patent system works. I think it's also important to distinguish between companies that think of ideas, then implement them, thus innovating in product; and companies who simply patent the ideas and use them to sue. We call those "patent trolls".
For design (again, referring to visual, UX, UI, etc, and not to software architecture design), the problem is how to make X better, e.g how to make interaction with a screen better [1]. And the solution is the design - we use fingers instead of stylus.
I'm thinking this out loud as I'm answering. So, it appears to me that what I am saying is, you can copy the problem (app or say UX issue) to be solved but you shouldn't copy the solution (be it code or design).
> Also, you probably copied someone at some point anyway.
I feel like going into this might be a digression so I'll try to keep this short - a specific example, when I was building my first iOS app, there was a competitor that was starting to be very well received. I'd like to say that I took note of what they did right and give my own twist to how to solve the problems which they saw important to solve. And I have specifically steered away in cases where it look like I couldn't come up with a better version, even if the replacement I had to use was not as good - a particular example was I have not to this date implement pull-(release)-to-refresh verbatim using any of the off-the-shelf OSS components in my app despite the original inventor giving permission to do it. So I do walk the walk.
Or maybe I did copy. But even if I smoke, I can still take the stand that smoking is harmful.
[1] I'm specifically referring to focusing on a finger/touch-based experience vs. using a stylus. I'm not claiming that Apple is the absolute first to do it since I had often used my thumb/finger instead of my stylus when I was using my Treo, but this is a good example of someone innovating.