Honestly, I think as long as it's recognizable, it should be okay to adjust to suit the game, website, etc. Obviously for Coil.com, the styled C with the black background is their preferred logo... so if you can keep it the same that would be ideal... but if you had the styled C on a dark purple background that could work.... especially if it was clickable.
I think at the end of the day, companies would rather receive attention than be ignored/not included (unless it was going to hurt their brand)... but as people have already mentioned, I'd always try to run it by the company before releasing to the public.
Agree, extra "free" attention is usually good, as long as it's not ruining the overall image of the given company.
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