A quick visit to the recent history of bike rims might help here:
When some manufacturer of bikes rather than rims invented the 29er, which is basically a touring or utility bike with wide balloon tyres, the technical side of ERTRO (European Tyre and Rim Technical Organisation), the industry body, was horrified to see some manufacturers, in a hurry to share in the new market created, cynically put 50 and 60mm tyres on 19mm and even a few narrower rims. ERTRO then urgently reminded everyone of existing guidelines, which were that the minimum rim width over the tyre bead-retainer ridges (not the outside of the rim) should be at least 40 percent of tyre width. Schwalbe, whose tyres many on the Thorn group regard highly, later published similar minimum rim width to tyre width recommendations.
The rim makers screeched to high heavens about not having the capital to invest in new molds and warehousing for a fashion flash in the pan soon to be overtaken by the next fashion flash in the pan, which is what many took the 29er craze to be in the beginning*, and ERTRO, an industry body representing the manufacturers, not the cyclists, hurriedly backed off and basically added an implicit "or whatever you like".
Thus the danger, to which in the original instance ERTRO responded, remained that wide tyres on unsuitable narrow rims would have to be more highly inflated, and would thus stand a greater risk of coming out of the retainer beads in high-speed cornering or even bursting the cheaper narrow rims apart.
Eventually responsible bike designers and manufacturers specified more and more wider rims as it became clear that the 29er had come to stay, as I forecast when it first appeared. The rim manufacturers responded with wider rims.
I tried a 60mm Big Apple on the 19mm no-brand Chinese rim into which an electric motor had already been laced, and nothing awful happened, except the bike was slower because the slight deformation of the Big Apple by the narrow rim put less rubber on the road, and on the downhills I slowed down considerably compared to my normal standard of letting her rip, because the bike didn't feel stable or particularly responsive to tightening the steering in corners (too much understeer). Perhaps not a big deal if you're poor and cannot afford the sometimes substantial premium for high quality wide rims; the likelyhood is that you will still think you're going faster than on narrower tyres, on which you could never approach the downhill speeds and security of a true 29er.
My personal opinion is that ERTRO's 40% of tyre width rims are still a bit iffy, but again, most cyclists have never gone as fast as you can go on 62mm tyres on rims with 25mm between the bead retainers, which are today relatively available and certainly comparatively cheaper than when the 29er was born, so most cyclists are likely to be satisfied.
The mental arithmetic sum for the minimum recommendation of 40% is rim width across the bead retainers times 2.5, thus if you have or can source a 25mm rim, 25mm x 2.5 = 62.5mm. Or, you have or can source 62mm tyres, you need a rim of (62/2.5)mm which rounds off to 25mm rim width across the bead retainers.
Below the footnote, there's a table of rim and tyre widths for the minimum ERTRO width recommendation to fit the widest tyre, both numbers in millimeters, in all cases where fragments remained rounded downwards because these rim widths are minima.
*Not me. For me the 29er was one of those very rare true engineering advances in bicycles -- it was clear me as an old racing car chassis developer that, if properly engineered, it would make for a faster, better-handling bike than the 37/38mm tyres I regarded as a poverty limitation on the bikes I had before the 29er; it also reflects my marketing background, because I further argued that if cycling were to grow, it would need to grow into sections of the population who didn't care the bat of the eyelid for the privations that came with bicycles but would demand both comfort and exceptional security for their commute or Sunday ride.
ERTRO Generalized
Minimum//Maximum
Rim Width//Tyre Width (all mm)
18//45
19//47
20//50
21//52
22//55
23//57
24//60
25//62
26//65
27//67
28//70
29//72
30//75
31//77
