It kind of comes down to how you think about it. In American English, you start with the total, e.g., £200. Then, you deduct the deductible (e.g., £50). So, you are left with the amount you can claim (£150). In contrast, in British English, you start with nothing* then, there is the excess (£50) and anything in excess of that amount you can claim (£150) towards the total (£200).Her footnoted comment is that the differences in perspective are not terribly surprising, given the stereotype of Americans as positive-thinking and the British as, well, not. I'd explain excess slightly differently: you start with a claim for £200. The insurance company gives you £150, so your claim exceeds (is in excess of) the settlement by £50. I'm not sure that this is any less 'positive' in its perspective than deductible is.
On another insurance note, in BrE, you're more likely to see some insurance products or companies with assurance in their names, rather than insurance. One particularly sees it in the context life assurance (vs AmE life insurance)--but this is rarer and rarer. On the differentiation of assurance and insurance, the OED says:
Assurance is the earlier term, used alike of marine and life insurance before the end of 16th c. Its general application is retained in the titles and policies of some long-established companies (e.g. the London Assurance Corporation). Insurance (in 17th c. alsoThat, happily, is about the extent of my experience with insurance-related terminology. If you know of any more, feel free to relate your examples in the comments.
ENSURANCE) occurs first in reference to fire (1635 in INSUREv. 4), but soon became coextensive with assurance, the two terms being synonymous in Magens 1755 (see ASSURANCE5). Assurance would probably have dropped out of use (as it has almost done in U.S), but that Babbage in 1826 (see quot.) proposed to restrict insurance to risks to property, and assurance to life insurance. This has been followed so far that assurance is now rarely used of marine, fire, or accident insurance, and is retained in Great Britain in the nomenclature and use of the majority of life insurance companies. But in general popular use, insurance is the prevalent term. Mr. T. B. Sprague, followed by others, considers assurance, assure, assurer, etc., the proper words for the action of the company or persons undertaking the risk, insurance, insure, insurer, etc., for that of the person paying the premium. This would be in some respects a useful distinction, if it could be carried out; but it would leave the members of mutual societies at once assurers and insurers.