The Fluke is safer. It has a proper fuse which will blow if you accidentally connect it to the battery terminals when it's set to measure current. Cheap meters often don't have a fuse or one with a poor breaking capacity so may smoke and catch fire if connected accross a car battery.
Your statements do bring up a good point in favour of better made instruments. Reliability, robust construction and the ability to withstand accidental overload are the major differences between a worthwhile instrument and a $50 cheapie. Substitute resistance for amps in a repeat of your previous scenario and it's often a difference between a flashing error display and a now dead instrument.
It's stupid to have a $1000 instrument banging about in an automotive tool box when all that is required are simple measurements. A high impedance instrument can also lead the inexperienced to erroneous conclusion in that environment. It is certainly sacrilege to have a highly desirable instrument bashed about in the back of a van, Even so, these are not environments for dubious cheapies. Rubbish meters are false economy, and after replacing your second or third in short succession a basic Fluke or similar has become a much better proposition, especially when wasted time is factored in.
For routine electrical or auto electrical work a basic Fluke or similar would be the wise choice, with the range of available brands and instruments much wider than at the top end. There are many better priced models tailored specifically for these applications.
Rubbish meters belong in landfill, a good instrument isn't that expensive, basic name brand are instruments certainly there for under $200, with well made offerings to be had from lesser brands albeit without the instant recognition.
To suggest Fluke is the only quality manufacturer is ignorant, to question unknown instruments is prudent. A Fluke has been and still is synonymous with all the attributes of safety, durability, accuracy and repeatability. How far that reputation carries into the future will depend on the success of the current and future model range. Given the prevalence of grey market importation of lesser specified Chinese market Flukes, it is likely the Fluke reputation will diminish to some degree.