Re:
I smell BS.
It's a long time since I had anything to do with this, but Trade Mark law and Intellectual Property rights prevent a manufacturer from using a brand name or something very similar on a different or inferior product.
I suspect it is in there somewhere, but you'd have to dig pretty deep to find a clause that prevents someone reproducing graphics used by a brand, that's not really what the law is there for. Plus, if the frame being refinished is a Holdsworth, then PX could not claim infringement, as the frame could be proven to be a Holdsworth. If you were trying to pass off a BSO as a Holdsworth, they would have a valid claim, but even then the law is not really there to prevent a one off, it is there to stop one manufacturer ripping off anothers designs, logos and products.
I suspect that PX are banking on frightening off a small firm / sole trader like H Lloyd with threats, knowing that the smaller company will not risk testing the larger companys mettle.