I’ve never heard that. Before we moved to a house with a gas stove (YEAH!), our electric range’s burners were constantly covered in aluminum foil (for ease of cleaning). We never had a problem, but then, we are just one family.
Aluminum is flammable, but at higher temperatures that you will likely encounter on your stove. If you are concerned, most hardware (and many dollar-type) stores sell pre-made burner pan liners. These too are aluminum, but of a heavier gauge than foil.
Aluminum is not flammable. Once aluminum reaches its melting point which is about 600 degrees Celsius it will melt, not burn. It is likely as a drip catcher that you won’t have a problem. Some of the better stove tops can get pretty hot, well over 600 degrees celsius but the aluminum is not in direct contact with the burner if electric stove or the flame if gas. You should be alright, but you don’t need to worry about a fire.
I heard a great tip on this subject. Since it’s nearly impossible to keep drip pans clean (even with foil…it rips), you should save yourself the trouble, and buy an extra set of them. Use one set for cooking, the other for looking. In other words, when you’ve got company coming, swap out the messy ones for the perfect, clean ones. Never cook on the clean set. I haven’t actually gotten around to doing this yet, but I plan to!
I would think that aluminum foil is designed for use in the oven/stove. The grocery store sells aluminum drip pan liners. I’ve lined drip pans with foil for over 25 years with no problem.