I thought exactly the same thing and nearly started a thread on it myself.
Even if he'd just said "He is determined to fight this" and left it at that, it still has the implication that others don't bother to fight it, when for some people, their own physical health/mental health/personal circumstances and vulnerabilities mean that they just don't have the strength to stay positive in their adversity.
To go the whole hog and say that he will pull through BECAUSE he is a fighter is a real slap in the face to the families and friends of all those who don't pull through from whatever illness.
It's one step up from when some people don't appreciate their privileged circumstances, backgrounds, education, abilities, good health etc. and declare that all poor people "just need to pull their finger out and work harder like I did after my parents left me enough to buy a business outright "
It's also a big slap in the face to the dedicated NHS staff (even when verbally accompanied by praise for them), as it seriously downplays their role in helping people's recoveries and effectively turns the blame on to them when, in spite of everybody's very finest efforts, recovery just isn't possible.
What would have been wrong with just "He's in good spirits, the amazing NHS staff are doing everything they possibly can and we're all very hopeful about a swift recovery" ?