SSD's are a different beast. There are locations on it that are not accessible by user level tools like Disk Utility. If the SSD controller has detected a location goin bad, it will mark it bad after relocating its data to good location. That bad location will still have the data on it, but is no longer accessible by tools like Disk Utility. So, using Disk Utility to erase the drive, or "overwrite with zeros" will only affect the portion of the SSD that is accessible by the utility.
I prefer to use something like PartEd Magic (I use the ISO I got before they started charging for it,) boot the system from it, and use its secure erase utility to do the job, as it sends an erase command to the controller on the SSD, and the controller is then "supposed" to erase all data on the drive, including data located in those areas that are inaccessible by user level tools like Disk Utility.
However, there are reports that not all SSD controllers do a good job of that secure erase. This is why, in the end, my main recommendation is to turn on FileVault if security is that important to you.
There is also the fact that when you write zeros across the user level areas of your SSD, you are technically filling it up with data, even though it's all zeros. So, your SSD will take a performance hit compared to if it were secure erased. This is not an issue in this scenario, as the OP's friend is going to return the system and get a new one, and Apple will (hopefully) do a proper erase on the SSD anyway prior to selling it as a refurbished unit.
The general moral of all this is that SSD's are not like HDD's. They require a different method of handling to get the same types of erasure jobs done.