You might notice that the URL you're linking identifies the expression as "need [your] head examined". On the page itself, there is a usage note saying "UK also need your head examining", of which no examples are given.
> Passival my arse.
Do you see this construction as different?
Wikipedia:
> Another construction sometimes referred to as passival involves a wider class of verbs, and was used in English until the nineteenth century. Sentences having this construction feature progressive aspect and resemble the active voice, but with meaning like the passive. Examples of this would be:
> The house is building. (modern English: The house is being built)
> The meal is eating. (modern English: The meal is being eaten)
> This passival construction was displaced during the late 18th and early 19th century by the progressive passive
Oh I'm sorry, I thought you'd find it funny. "X my arse" is another British idiom (but "Passival my arse" is novel). Yeah "need your head examining / looking at" are both quite common; as you say the online dictionary I linked gives it as a variant and you can confirm via quoted Google search strings that they're used.
As for whether "need your head examining" or "needs its functionality amending" are related to the examples you're giving, it sounds like you perhaps think more deeply about grammar than I do, but I would tentatively say not. Your examples are "<noun> is <present participle>", whereas "<noun> needs its <noun> <present-participle>" seems different to me.
I'd say the thing you're commenting on is normal, if not altogether correct, in British English (Where are you from? I'm from the UK).
https://dictionary.cambridge.org/dictionary/english/need-hea...