Yes, this is valid, and your logic is correct. However, it is not invincible. They can always be returned to the hand, or they can be banished, unless of course you have monsters or spells/traps to prevent this. There
The most important part of a Trap Monster that concerns this is the part that says: "This card is also treated as a Trap Card" This means that even though it is a Monster, it is also another flaw: the monsters can be affected by card affects. Thereforetreated as a trap, something like Divine Dragon Knight Felegrand can be use to do this hence being indestructible.
Anything that the rulebook doesn't state makes it valid.
Now... a card that stops it affects from being negated