OK I feel a bit better, thanks. I'm grateful for all comments, including the point about fire retardant properties, and for the advice about attending while charging etc. I might just buy a barbecue for £10 to store the thing in indoors while I'm not in and while charging.
I don't think it's actually accurate to say a concern is paranoid though. I think until you know something is safe, a concern for safety isn't paranoid. Drivers imagine they "know" it's safe to drive round blind country bends at 60mph because they've never had an accident before. They shut out any evidence which could trouble them, and we know what an awful attitude that is. It may be that my buying an ebike battery bears no kind of comparison to this sort of blindfolded attitude to risk at all, but if I've got worries then it's my responsibility to satisfy them, rather than just take the "meh" approach. Mainly because I like my landlord whose property adjoins mine.
I was partly worried to read on this very forum that if one dropped a lipo pack, one might have 20 seconds before it would be pouring vigorous flames, and so worried that if encased lion battery packs could have even a small fraction of the same volatility, then there could be issues given I'm averagely clumsy.
What happens if you drop a L-ion battery pack which is encased in plastic etc?
As for gadgets with lithium batteries which don't burn, I know that we all have lots of them, but I'm not sure that's comparing like with like (and I mention this just to share my thought process - it's a sort of pedantry so I apologise if it seems catty).
The original designs for gadgets likely had millions if not billions spent on researching and testing design safety and manufacturing-process design, whereas retail ebike batteries I suspect are often assembled in a small workshop and in small numbers where people buy in batteries (with provenance and quality sometimes difficult to guarantee), and BMSs which haven't had the kinds of investment in their original design and manufacture as goods designed for Western markets with genuine CE/other similar certification; and then those workshops, often one or two people, may fit them together themselves under who knows what conditions. I've read about people buying from some stores where cells regularly just fail to charge, so I see no necessary reason why failure would be confined to non-safety-related issues.
That's setting aside the issue of much greater discharges/loads/energy storage etc than ordinary consumer electronics.
And one more thing: Dreamliner. Dreamliner seems to relate to charging issues - something people confirm here is a risky point in the usage cycle. Yet how can I be sure that any dangerous occurrence during charging, will actually make itself apparent while I'm charging, and not later when I'm not?