“Foreign names can get inconsistently mangled in Czech”—but to my knowledge Czech doesn't attempt to preserve foreign spelling, with e.g. letters Ñ or Ø. Czech adapts spelling to native pronunciation, which is my entire point. The ‘mistake’ here is that English keeps doing things backwards, and ‘Čapek’ is just one example here.
I had to look up the usage of ‘W’ in Czech, and Wikipedia says: “The letters Q, W and X are used exclusively in foreign words, and the former two are replaced with Kv and V once the word becomes ‘naturalized’.”
There's a close example in Russian: John ‘Dr.’ Watson's surname can be pronounced either ‘Vahtson’ or ‘Oo-ohtson’, but there's no intermediate sound like English ‘W’ in Russian (and no letter for it). So the name was spelled either of the two ways in print until it became settled on ‘Vahtson’ (‘Ватсон‘), which fits more naturally in the rest of the language. I expect a similar thing to happen to ‘Williams’ in Czech, though I'm surprised that they still have trouble with it at all, as the surname is old and widespread. However, current strong influence of English can mess things up—people, including myself, use English pronunciation even in the context of a native language.