Does MISSINGNO. actually destroy saved game files?
As directly quoted from the MissingNo. page on Bulbapedia:
"Missingno.'s appearance in-battle allows the item duplication glitch, which increases the number of items in the 6th Bag slot by 128 unless the number of items in the slot already exceeds 128.
Encountering Missingno. has been known to interfere with the save game data in various ways, such as adversely affecting the Hall of Fame saved data and (if its stats are viewed) messing with some graphics until the stats of a non-glitch Pokémon are viewed. When a Trainer battles with Missingno. in their party, both the Trainer sprite and their Pokémon's sprites will be scrambled, and all other sprites will be reversed. Viewing the stats screen of a non-glitch Pokémon will remove the effects. In Pokémon Yellow, capturing Missingno. will cause multiple player sprites to walk around the screen. "
Nintendo has an official description of Missingno. listed in their Customer Service troubleshooting section. A direct Nintendo quote:
MissingNO is a programming quirk, and not a real part of the game. When you get this, your game can perform strangely, and the graphics will often become scrambled. The MissingNO Pokémon is most often found after you perform the Fight Safari Zone Pokémon trick. To fix the scrambled graphics, try releasing the MissingNo Pokémon. If the problem persists, the only solution is to re-start your game. This means erasing your current game and starting a brand new one."
TL;DR: No, it just messes with your save files, permanently messing them up, but not actually deleting them.
After a bit of research I have found a lot of information with little verifiable proof.
MissingNo is created by an error handler which replaces any unknown pokemon ID with MissingNo. MissingNo is commonly confused with 'M' or 'M-Block' but is not the same pokemon, nor the same glitch.
From Missingno. Master/Glitch Rumors:
Seeing or capturing Missingno. will wreck your game.
FALSE
Probably the oldest rumor out there. It still holds strong amongst newbies, as in this day and age, the old Red and Blue versions are conking out due to old age and people are quick to blame Missingno. for this. Missingno. scrambles the sprites and screws over the Hall of Fame, sure, but the first is easily fixed and the second is actually entertaining. This is the extent of Missingno.'s damage to the game.
That being said. As the game shows the same corruption across saves this proves that the game save itself is corrupted. The two main corruptions known are the garbled display (which can be easily fixed), and corruption in the Hall of Fame (which can't). Even if the save is corrupted in a non-chaotic fashion, there is no way to verify that the savedata will remain stable across the rest of the game without re-running the entire QA process on the new corrupted save.
No, MissingNo. in Red and Blue Versions affects saves, but only the area containing Hall of Fame data.
When encountering any Pokemon in the game, save bank with Hall of Fame data is opened. The reason being that the area just before Hall of Fame used for decoding Pokemon sprites - Game Boy doesn't have enough RAM to hold decompression buffers, so the game uses on-cartridge memory for those.
However, MissingNo. sprite goes outside of sprite buffer, and overwrites Hall of Fame data. The sprite is constant (read from ROM, not RAM), so it always corrupts the same way, and due to that there is no risk of it doing something unexpected.
If you won't view Hall of Fame on PC, MissingNo. should be completely safe. However, Hall of Fame has garbage data, which means it can load other glitch Pokemon that can corrupt information in RAM - but this is likely to either do nothing or crash the game with Hall of Fame data open for saving so there is no risk of losing the save. It's possible to repair Hall of Fame data by beating Elite Four 50 times without seeing MissingNo.'s sprite.
MissingNo. also sets highest bit of sixth item in inventory when seen. This increases its count by 128 unless you had 128 or more of it already. This is because the code to handle seen Pokemon considers Pokemon 0 to be 256, and then goes beyond area of RAM reserved for seen Pokemon, accessing the item data.
Garbled sprites after seeing MissingNo. are caused by leaving the flip flag set after decoding the sprite. This normally should never happen, but it did, because MissingNo.'s sprite is not intentional. Seeing a sprite in Pokedex should reset the state of this flag.