I think it matters.
"Bitcoin" is easily recognizable as an alternative to "bitcoin" and it isn't necessary to use the nonstandard or unofficial variation of "BitCoin." What would be the reason for capital C?
Perhaps for related naming schemes these would be appropriate also then?
MoZilla FireFox
MicroSoft InterNet ExPlorer
AdoBe PhotoShop
GnuMeric
AbiWord
AudaCity
RhythmBox
KonQueror
What detrimental effect does miscapitalization of a single letter cause? I really don't think it's going to confuse anybody.
The same reason just five days ago my mom was bursting into tears* in utter frustration and disappointment that Amy Goodman of Democracy Now! misspelled her name with a 'C' instead of an 'S' even after just twenty-nine seconds prior my mom had communicated to Amy Goodman that her name is specifically spelled with an 'S.' Spelling and capitalization is important and serious business.
* Note that my mom was already bursting into tears and in utter frustration and disappointment in me because she saw my facial expression in reaction to the amazingness of Amy Goodman's talk and she was jealous and mad at me that she hadn't established a similar reaction from me due to her not being as amazing.