The first one is definitely a scam, but there are cases of having a very mild condition which with a cane is greatly eliminated, such as if you have vertigo. If very mild, you can walk without the cane but you will not be walking in a straight line.
There are other things that could be wrong with you as a single issue or as part of the vertigo issue, such as your eyes/brain are not capable of canceling the vibrations everytime you take a step. Unlike normal people who have a steady eyesight while walking, the person no longer capable of doing that will see everything vibrate with every step they take. If mild you can "deal with it" without a cane, but it will not be walking 100% like a normal person. With the cane the risk of fslking is greatly eliminated as it gives extra support.
If you very essily lose balance, which comes with the territory of having even mild vertigo, then you will not "need" the cane most of the times you have it except in those sudden times when either there is a bump or a sudden unseen drop on the pavement where a normal person with normal reflexes will compensate or if trips will quickly rebalance. If you are more prone to lose balance and/ir your reflexes are not what they used to be, simply having a cane will prevent falling in case you trip as it gives extra support and something to hold on.
So while the first one was definitely a scam, there is a chance the second one isn't. It may seem to be one if the person is perfectly fine, but anyone with a mild case of vertigo or mild but higher than normal possibility of losing balance, in a situation like in the second the person can run in short distance to avoid getting hit by a car.
Many people think someone needs to be severely impaired to need a cane 24/7, but in reality most people with a cane have a mild case. The thing is that it's better to have a mild case and carry a cane despite you will not need it 99% for that 1% of the time when you will need to avoid a fall. It certainly is better if you have a mild case, don't carry a cane and then that 1% hits, you fall and perhaps there are broken bones, punctured organs, internal hemorrages that untreated could lead to death, concussion, cracked skull, hit the head so hard on the pavement that you go unconscious, etc.
Al, it takes is to fall once and the wrong way to put an end to your life. That can literally take less than half a second and could had been avoided if only you had a cane.