the engine will catch fire only if it not running according to VW specs, this happens maily due ot negligence from the owner or the mechanic. i drive my cars in peak summer with a VERY heavy foot and so far no issues as it was built correctly. the main reason for them catching fire is down to the fuel line not being secured with jubilee clips, time comes when the pipe ages and dislodges from the filter or carb and sprays fuel on the engine. simple routine checks can help you avoid most issues.
this doesn't mean that they will be bulletproof though. i've been stuck on the roadside with a snapped accelerator cable, but i just idled the car to romanos house where i got her up on a ramp and fit a new one myself (you must carry spares with you).
experience will eventually get you used to getting the car back on the road in a few minutes and it's a steep learning curve in the beginning. recently the 1303 used to die as soon as i touched th throttle (idled fine), i tied the simple trick of sticking my hand on the carb top when the engine was running which removed the gunk stuck in the carb and within a few seconds the car was fine.
old car have quirks but if maintained correctly (and once all the problems are worked out) there is nothing stating that they cannot be reliable (i drive my 1303 to office from time to time too and i've never had issues.
if you have an inherent fear of the car catching fire keep a fire extinguisher in the car (i do)
that's what funnels are made for