what does this error message imply: fatal: unable to access 'https:URL': Peer's Certificate issuer is not recognized?

One possibility would be the absence of Certification Authority certificates on your system.

If that is the case, you can add those as described in this answer.

This is better than ignoring said CA (env GIT_SSL_NO_VERIFY=true git clone https://github...).

In the specific case for this OP, Brandon comments:

I am running 64 bit fedora 19 and, as root, I went to /etc/ssl/certs and saw there was a makefile, so I ran it with a different serial i.e.:

$ make SERIAL=5

Tried git and it worked.

This works for me

git config --global http.sslCAPath /etc/pki/tls/certs
git clone <repository>

This works for me

git config --global http.sslVerify "false"

git clone < repo-url >

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