My experience with my A7rii is that lenses, focus ability, and stability are far more critical than with my older, lower MP bodies or with film if you're looking for peak sharpness and making full use of the resolution (large prints or 1:1 digital images). Stablised bodies and lenses help, but a more stable platform (even a basic tripod) definitely improves things.
You can definitely shoot without, and I do all the time, but make direct comparisons between tripod and hand held of the same thing at the same settings and you'll see a difference.
I agree with Phil here.
Using a tripod and a remote release will give better results than handheld, even with the various forms of lens and body stabilisation available today.
Even using a mechanical shutter can cause vibration and degradation of image quality depending on the shutter speed used.
That said, excellent results are possible with good handheld technique.
Some people do struggle to hold a camera still when shooting.
Your friend is a female and the truth is that some women do struggle to hold camera/lens combinations still when shooting. I would say that her comments exactly reflect her experiences and her pursuit of image quality necessitates the use of a tripod and remote release for any kind of image quality.
On a larger note there is something of an urban legend that digital imaging makes getting excellent images easier. In certain situations this is true. However, high resolution sensors and the newer lenses developed to take advantage of those sensors has created, IMHO anyway, a welcome contradiction to the legend. Very close attention to detail and any very good camera technique are required to get the best out modern photographic equipment.
Largely, we need to think how our medium format brothers used to think when shooting. It appeared that the size and weight of those camera/lens combinations necessitated using camera supports however, really, the resolution of those cameras was always the more important reason for using a big and steady tripod. (Of course a big heavy camera does require a larger more robust tripod than a small light camera.)
The fact that we now have such huge resolution available in much smaller form factors may have fooled certain people into thinking that hand-holding these cameras will always work. It doesn't! The issue was never the weight of the camera rather it is the resolution that limits the situations where hand-holding will give acceptable results.
Again, some people will still get good results handholding when others cannot, but the limits remain.
There is no point in shooting with high resolution cameras unless one is planning to exploit that resolution. If all one is planing to do is post low resolution images to the web or on social media then get yourself a 12 MP camera. 40 or 50 MP cameras were developed for those people who want to print large - very large.
In addition, these cameras are also not primarily developed as sports/action/wildlife cameras where hand-holding is common and often the best camera support one can use is usually a monopod. In, general, high resolution cameras are developed for a slower, more contemplative, shooting style where the use of a tripod and remote release makes sense. Obviously, if the light and the type of shot desired allows a high shutter speed relative to the focal length employed then good results can still be attained by shooting handheld. Nonetheless, visibly better results will be attained in nearly all circumstances, using the same camera settings, if a tripod and remote release are employed.
The question that every individual needs to ask is how good is good enough. Your friend clearly has high standards and for her can only be attained by using a tripod, and probably a remote release as well. Your standards may be different...
Nonetheless, in a lot of situations, I would be advising a tripod and remote release, and even a large heavy sandbag draped over one's camera and lens to reduce vibration from any cause. Attention to good technique, whether handheld or not, is absolutely key to modern high-resolution digital shooting...
Tony Jay