Why aren't my profile and bashrc files hidden?
However, I've been able to follow these tutorials just fine, I just
  edit my profile file instead of .profile, and bashrc instead of
  .bashrc.
  
  Is there a reason why these files are not hidden for me? And does it
  actually matter?


Yes to both questions.

Basically .bashrc ≠ bashrc 

(same hold true for the other files mentioned as well)

A Unix dot-file (.filename) is treated as a hidden file.  The dot preceding the filename is actually part of the filename itself; it's just interpreted by the system to be hidden.

To look at it another way, it's as if you used any other character at the beginning of the filename (a dash for example).  -filename is a very different file from filename.

So, when you say you've edited your profile, your actually editing the wrong file, you need to edit your .profile.

There's an excellent post on StackOverflow that explains when to use .bashrc and  .bash_profile 


  So shouldn't there be an error from the terminal/bash initialisation
  program that's looking for .profile and .bashrc, since I only have
  profile and bashrc?


You're not getting an error message because there's no error


these files are optional
.profile and .bashrc don't exist (see above)