That's one aspect of it. Dilute strong acids and base are "relatively safe".. compared to say concentrated strong acids and bases, but they still demand respect. Another aspect of the hazards of a true WTA purification are some of the procedures and the equipment required to pull it off. In one such procedure, innocent lack of experience and knowledge (simply not knowing what to expect, when to expect it, and what to do about it so that it doesn't bite you on the ...) can lead to a pressurized release of liquid... which might well be acid or base at pH 1 or 13.
If you're adverse to soap-boxing, skip the rest...
"pH 13 caustic meet eyeball..." In my early days of work-study back in college, they made me watch videos with slide after slide of so much chemical burned skin and grotesquely f'ed up eyeballs and the like that I eventually started to get ill. I mean, after the first half-hour, I kinda got the message.. but they felt they needed to drive the point home ad-nauseum.
What would you rather get on your skin and not realize it? Strong acid or strong base? Would you rather get a good whiff of HCl (strong acid) or HF (relatively weak acid). If your first instinct is the Google for the answer, then you'd better think twice about about the evolution of your kitchen lab. (I'd much rather get the acid on me than the base, and HCl will mess up your day, but HF will make you dead... I don't currently work with HF, but it scares the hell out of those around me who do). Do you know emergency procedures for exposure? Do you have an eyewash? Do you know what an eyewash is? Would you know how to use one?
One aspect of safety that I've come back to on several occasions is the often heard, "I'll be safe!". The trouble is, being safe can sometimes involve knowledge and experience. More properly, "I'll be safe" too often simply means, "I'll be careful!". Careful and safe are not equivalent. One can be extremely careful, but a failure to appreciate a critical aspect or two can render one extremely unsafe.