If that were the case we'd all be in trouble.
I've got wine, champagne and beer yeast all sitting next to each other in my brew closet. And have had no issues ever with it.
My Fermentation Closet: #1 Grain test Pale Ale 1 (dry toasted) #2 German Apfelwein (hard cider @ 3 months) #3 Grain test Pale Ale 2 (soaked in sugar solution then toasted) # 4 Grain Test Pale Ale 3 (soaked in water then toasted) #5 1-gallon Date Wine #6 Old Ale Brewed on New Years, then oaked for a week and racked to a tertiary to bulk age).
One thing to remember, whether or not what what you have heard is true, is that each fermenter is 1) protected by an airlock, letting air and co2 out, while keeping nasty stuff from getting in, and 2) Beer, and really anything in the initial stages of fermentation, is protected by a layer of co2 filling the fluidless spaces in the fermenter and cushioning your stuff from particulate matter.