Q: Has anyone recieved a virus warning from safari with a number to call?

Sadly you have fallen for a SCAM.  Do not pay them any money.

Since you let them access your Mac,

YOU SHOULD ERASE YOUR HDD AND CHANGE ALL OF YOUR PASSWORDS!!!!!!!

Then reinstall the OSX and user data from your backup.

Ciao.

It may also be a good idea to contact your credit card companies and  your bank as well.

Ciao.

Just responding to stress the answer that OGELTHORPE has given you... you must erase your hard drive and reinstall everything from scratch (or restore everything from a backup made prior to giving these scammers access to your computer). There is no other way to ensure that they haven't done something malicious to your computer while they had remote access. Anti-virus software will not to the trick, and many techs will "clean" your computer for you, but unless they are true security experts, they won't be able to actually do that.

See: A Browser Pop-up has Taken Over Safari.

(Note that I am affiliated with that site, and some pages contain ads).

This happened to my parents last night and they did not realize it was a scam, and proceeded to pay for this company to install some sort of ad blocker program on their computer, through remote access to their computer. They turned their computer off once the called ended and within an hour realized it was a scam, and called Apple support who told them to come into the store and that they would need to erase the hard drive. However, at the genius bar, they removed all the programs that were installed and did a scan for malware, etc. They were told that their computer is fine and they do not need to erase the hard drive; that because programs were removed scammers can't access the computer. I am skeptical because of the conflicting information. Unfortunately I was not there when these programs were installed on the computer so I don't know specifically what happened and what the scammer had access to. Should we trust being able to use the computer or is it possible that the scammer still has access to the computer somehow?

Thanks.

By erasing the HDD and reinstalling the OSX and user data, you eliminate any doubt.  I personally would do that.

Ciao.

Thank you, thats my instinct as well.

However, my other concern is the remote access issue. My parents' computer is linked not via wifi, but through a hard wire connection. Since the scammer had remote access, is there any concern with the IP address - in other words, would they need to reset the IP address or should this not be a concern?

Those swine need the software installed in the Mac in order to gain access.  If you have erased the HDD, you have no worries.

Ciao.