This is true on the relatively regulated world of the railway, where any ITSO card is (supposed to be) accepted by any TOC.
However you have to be a lot more careful with buses. I know it's not really the topic of this thread, but I feel it's worthy of mention anyway - it's often impossible to persuade bus company staff to load tickets onto another operator's card, except in cases where there is a scheme controlled by a PTE (such as TfGM's 'getmethere' cards) - even though they are technically compatible. Then there's the ticket machines, some of which check who issued the card before accepting it, refusing to accept cards other than those issued by that operator (there used to be some of those on the railway too but I think they're mostly gone now).
In short: ITSO on the railway generally works. ITSO on buses is a horrible mess with all paths seemingly leading to the passenger having to purchase a new card for every bus operator despite them all being compatible with each other.