I’d say, it’s ok both with «собой» and without.
The verb «покрывать» (“to cover”) is trivalent: ‘S covers O with I’.
Semantically, in this sentence, «гейзеры, горячие источники, лавовые поля и ледники» is I (indirect object), «почти вся территория страны» is O (direct object), and S (subject) is not defined.
But syntactically, «гейзеры, горячие источники, лавовые поля и ледники» takes the position of S (subject). So you need the word «собой» (“with itself”) to be placed to the position of I to show that the syntactic subject is an indirect object semantically. It is analogous to the using of -ся in verbs when you need a passive (the semantic direct object to be a syntactic subject) as in «звук произносится» (“the sound is pronounced”).
But there are verbs that do not require -ся. E. g., consider the sentence «Оркестр играет музыку громко» (“The orchestra is playing music loudly”). If we want to avoid the subject (‘orchestra’), we can say «Музыка играется громко» (“The music is being played loudly”), but more natural way is to say «Музыка играет громко» (“The music is playing loudly”) — ‘music’ is a syntactic subject here, while semantically it is a direct object.
The same is true for the word ‘cover’ (with its indirect object instead of direct one), so you can say (both in English and in Russian) “I covers O” with the same meaning as in “O is covered with I”.
So both variants, with «собой» and without, are correct.
(Sorry for the muddle and for my terrible English!)