possessives - “A similar hat to Jane” vs “A hat similar to Jane’s”

Of late I have noticed British people using the following sort of construct:

John and Jane make such a cute couple because John always wears a similar hat to Jane.

To my ear, that is ungrammatical, or at least nonsensical, because John seems to have mistaken his wife for a hat! John’s hat cannot be similar to Jane; it can only be similar to Jane’s hat.

For me, that sentence must therefore be recast as this:

John and Jane make such a cute couple because John always wears a hat similar to Jane’s.

That way the hat is no longer similar to her, merely to hers.

Is the former formulation actually grammatical, or is it a common mistake or simple carelessness? Doesn’t it confuse people? Is it fit for formal writing? How long has this been going on?

To the American ear, it sounds really messed up, like it is making a wrong comparison. It’s like they have forgotten about the possessive case, which is the only one that makes sense here.

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Edit

Here are actual “similar X to Y” instances by British authors, where one would expect to find “Y’s” or “that/those of Y” instead:

• In consultation, our members observed that other people with a similar disability to Mr Malcolm — perhaps with varying degrees of severity — would have been able to understand the sub-letting regulations. Great Britain. Parliament House of Commons. Work and Pensions Committee – 2009


• Dave had a similar accent to dumper truck man, so that’s who I thought it was. Explaining Colours to a Blind Man,
  
  David Hooper


• Believe it or not she was also Afrikaans with a similar accent to Anna, and, like Anna, she was not exactly a beauty. Paget's Progress: A Tale of High Adventure and Low Salaries, Dick Paget


• Auroville’s two or three thousand inhabitants, most of whom live in similar style to André, come from all over the world, as a brief glance at its telephone book made clear . . . In Spite of the Gods: The Rise of Modern India, by Edward Luce

But I still don’t understand it, nor do I know its history. When did the possessive go away, and why? Shouldn’t those all have a possessive there?

Answer

Jane is obviously not a hat, so it’s hardly confusing. I would analyse it as a rather extreme ellipsis in which the repeated noun and verb are both removed.

John always wears a similar hat to [the hat which] Jane [wears].

Whether I would write that, I’m not sure. Speech tends to be more compressed than written language, and it’s possible to take more time over being careful when writing. I might write Jane’s.