That can’t be it. The Basic interpreter could run the lexer on each line the user typed and store the tokens. You would lose the ability to print lines exactly the way the user typed them, but that isn’t a big blocker for the technology of the time.

Alternatively, the Basic interpreter could store each line as a combination of tokens and characters. Commodore Basic did that (https://www.masswerk.at/nowgobang/2020/commodore-basic-renum...).

I also think none of the microcomputer Basics stored keywords as ascii strings. It would both slow down the interpreter and use more memory.