Can you expand on "Not investing your money isn't safe either."?
When Icesave crashed in 2008, the Icelandic government refused to honour deposit insurance. I haven't followed the case, but it seems that depositors have started getting their money back. Cyprus confiscated 48% of all uninsured deposits in 2013, IIRC, at the time, they considered digging into the insured deposits as well. Greece was on the brink of leaving the Euro, imposing strict capital controls for over a month last summer. Had they left the Euro, all deposits would like have been forcefully converted to a new non-Euro currency, worth substantially less.
Finally, practically all mature countries (ie. those issuing cash you might want to hold) maintain some level of inflations, so you have a constant, negative return on any cash holdings. Even US treasury bonds and UK gilts, which isn't cash, and isn't "not investing", but is among some of the absolute safest investments, just barely keeps up with inflation.
Inflation is something you still need to keep your eyes on but was there ever a case (say, in the last 10, 20 years) in the EU were inflation was higher than the median savings account interest rates? I honestly have no idea but I know for sure since 2011 interest rates have always been higher than the inflation rate in the UK, for example. If this were a fact of savings accounts in the EU then inflation is not really something to be affraid of.
Obviously I'm using "save" as "making just a bit of a money while taking zero risk".
So except for the last two-three years of freak financial conditions (low interest / low inflation), holding cash would lose you money rather fast.
Not if they're in a greek account, for sure. They're better off in an account in a north-western EU country, but the Euro may still fail catastrophically.
Anyway, it's not about weighing risks, the GP was making a rhetorical point about being perfectly safe. Nothing is perfectly safe. For anything less that €100k, a bank account is a very safe place, and you can probably get a savings account that tracks reasonably closely to inflation. But it's not "making just a bit of a money while taking zero risk", it's "possibly breaking even with inflation, while taking microscopic risk". Unless you're only holding the money for a very short period of time, you're almost certainly better off sticking it in an investment vehicle with an acceptable (non-zero) risk profile.
I've experienced that. My parents experienced that. They had no "investments", kept their money in low-interest savings accounts, yet somehow their life savings was no longer enough to buy a used Toyota.
Want to get more strange? What about war? How much is your money worth in case WW3 breaks out? Hardly likely? sure. Is it possible? absolutely.
The point is, nothing is "safe", just different levels of risky.
I'm visiting Iceland in March, I'm affraid I might enjoy it a bit too much, enough to make me want to live there. :)