Veigar is not safe at ALL. Katarina, Zed, Fizz, Akali, and Yasuo are all incredibly difficult to deal with on Veigar. Any champion that has high mobility is a nightmare when you're playing Veigar, and that's especially true against champions that are very bursty. Champions with high burst also destroy Veigar because 1) he's incredibly slow, and 2) he's incredibly squishy. No matter what you buy on Veigar, you're going to get destroyed if an assassin gets close, or a damage mage gets their combo off. Veigar NEEDS to keep you at a distance, or he's going to get killed super quick.
Also, it's super easy to deny farm for him - if you out range him, prioritize forcing him to back, or forcing him to over-extend. Xerath is often perma-banned when I'm pay Veigar, because a good Xerath with poke so hard, that I either can't farm at all, or I am forced to stay on very low health, with no options to dodge if he either goes all-in or uses his ultimate.
If you get countered against him, he also doesn't have much when it comes to multi-target damage - his cooldowns are kinda high, and after he pops one champion, especially if he uses his ultimate to do so, he doesn't have much damage to take on another. That being said, jungle ganks are also a great response to Veigar, even if you don't out-range him.
Also, the early to mid game is your time to take him out, because by mid game he'll have stacks. Honestly, early game he's basically worthless. Yeah, his Event Horizon's stun is pretty long, but he NEEDS to either a) sacrifice stacks in order to conserve mana, or b) buy an item to alleviate his mana-hungriness. So, early on is the time to punish a Veigar player. If it gets to be 35 minutes in and your teams look even on the scoreboard, they aren't. Veigar is already most likely stronger than most of your team. What I notice a lot is that a lot of players that don't play Veigar often stay away and keep their distance at all times, because they aren't use to a champion being so much weaker than them early on like Veigar. Even at level 4 when he's got all of his abilities, they don't do anything, so that's the opportune time to kill him and keep him from getting strong.
Finally, Veigar is in a weird spot - no runes really fit his playstyle other than giving him things that he already has, instead of giving him new things that are more useful. Most of them give snowball potential, and he already has that built-in, so taking any runes that aren't utility based are a huge risk, because he'll just fall further behind if he loses lane.
This is from a Veigar player, so this is an in-depth look at the things that I'm afraid of, and things that I struggle with. This is just to show you that Veigar is not unbeatable. Also I can confirm that Veigar 1-shotting tanks never happens. Unless you're that bad and he gets super fed - like, Sorc Shoes, Void Staff, and 2000 AP fed. But other than that, I can firmly say that any tank that has built a spirit visage and any 2 other tank items is a problem for Veigar. That magic resist and all of that health is enough to tank at least 3 rounds of spells (that being 3 Baleful Strikes and 3 Dark Matters) and have a reasonable amount of HP left. The only real problem most tanks have against Veigar is that they can be kited, because they by and large don't have many mobility spells, and are prone to Veigar keeping them at arm's length with stuns, or forcing them to dodge Dark Matters to slow them down.