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I find it very hard to believe thay can do this with any kind of accuracy in all but the most isolated cases.

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Wow. google tempest or van eck radiation. It's possible to read the information on one computer monitor (CRT) of a line of terminals in a bank. It's like tuning into a TV signal, each monitor has a mostly unique signal which the decoder can pick up. Sometimes there may be interference, but in most cases it's possible. The radiation goes through walls just like a TV signal.

That said, I wouldn't be concerned about it. Very few people know of this capability or have the technical expertise/interest to try and do it.