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.