That chart is kinda outdated given modern RBAs and devices and coiling techniques but I am sure it will continue to haunt the internet for years to come as people who dont have a true working idea of how vaping actually works will continue to bring it up and reference it.
There are many facets to battery safety.
The biggest one for us pops up for Mech users, in particular sub ohming.
The general key is to not over stress your battery. Any given battery has an amp limit of what is safe and the further you stay under that limit then the safer you are (assuming all other factors are being dealt with safely)
using ohmslawcalculator.com you can input your voltage
(4.2 would be a liberal max for mechs assuming you are not stacking batteries or built some custom mod that uses a completely different battery that is commonly used)
then put in the resistance of your coil and hit the calculate button which will tell you your required amperage. If said amperage is lower than your battery amp rating (preferably much lower) then you are gtg.
As previously mentioned if you are using a regulated VV-VW device then you generally do not need to worry about this as much as the device itself has a built in amp limit which it will not (or should not) let you exceed.
Despite that, the trend for regulated mods is to use IMR type batteries as an extra precaution on top of the fact that many vapers have both mechs and regulated devices and having a battery that is appropriate for either is always a good thing.
Now if your battery question was not related to that please clarify and we will bring you up to speed.