It does make sense.
Disclaimer: I am not a licensed medical practitioner, so if anything that follows concerns you, please discuss with your GP or specialist. Any concerns about the equipment you have been provided with by your employer should be raised with your line management or health and safety department.
The article said:
"Why the iPhone is a worse culprit than any other mobile phone is unclear."
"The iPhone is almost entirely controlled by the touch screen, the very very least amount of effort is still enough to register on it.
How could this possibly cause more strain than actually depressing buttons- which would require more force???"
Although it seems counter-intuitive, touch-screens and similar "zero-force" buttons/mechanism actually result in a greater pressure on the finger.
With a normal button, there is a big difference between pressing and not pressing. This means that you can relax up until the moment of depression.
However, with a touch-screen, the slightest contact can result in an accidental click, and slips and poor contact result in unintended actions. To avoid this, the user learns to tense both the flexors (bending muscles) and extensors (straightening muscles) in the fingers. The two muscles then fight against each other and strain the finger and arm slowly, over time.
The high sales of mini travel mice are a consequence of this: people hate trackpads as they cause finger-pain.