But the bandwidth limit of any line is still the same, no matter how you divide your data between headers and payloads inside the packets, so jumbo-frames have exactly zero impact on available bandwidth and its limit. A kink in the cable would do more for bandwidth in most cases.
The thing is that if he gets such a large difference, he has alot of other problems, may be a very old nick that doesnt off-load the checksum properly, etc. Any decent PC today, if you have hard-drive bandwidth available, shouldnt have any problem at all pushing 98%+ Utilization on a gigabit line. That is a bit over 100MB/s.
The thing is, copying files are not a good test of bandwidth, its a test of end to end application use. And that includes hard drive speed, interfaces, filesystem, transfer protocol, network and sharing protocol, etc.

If you look at that image, the first parts are a filecopy first from my fileserver, writing to and than reading from my secondary drive, a velociraptor. The second parts, are the same, but first writing to, than reading from my main drive, and SSD, and if you know your SSD's, you could probably guess the model. The result is... that I need to defragment my velociraptor, since it usually does 100MB/s + on sequential reads if it doesnt have to seek. My SSD does much better. The fileserver is a 4 drive raid 5 array capable of 250MB/s or thereabouts.
A better test is something like iperf that can generate TCP and UDP streams in memory and connect to an endpoint. It's open source btw. And if you need a graphical front-end I can recommend jperf which makes the result abit easier to present to people.
Even better is programs like chariot that we used at work that can tailor specific stream and patterns including errors to see that a network handles everything correctly. And even better than that are the nifty little dedicated boxes with 10Gbit fiber interfaces that you connect to the network that does the same thing, but just a heck of a lot more of it. That said, I watched a few people miss a tiny detail one time during such a setup and the result was, never try to enable port-mirroring on a switchport passing 10 gbits of traffic with 64 byte packets, that will make your tests go awry. On the other hand, it does does work decently with 1500byte packets.