Most Japanese people don't know much about Japanese verbs and can't explain how to inflect them. I suppose English speakers are the same with English.
At Starbucks the other day, I met my language exchange partner. The subject of Japanese verbs came up and I found myself explaining what I know about them, and how to inflect them. She seemed quite amazed that such a thing even exisited.
I explained about the 3 groups for verbs which I have been taught, and how depending on the group, the inflections will be different. If I hear a new verb, I naturally (not quite so forced as when I was a beginner) guess the group in order to inflect the verb. However, this isn't always so simple. For example, verbs like 起きる and いる are group II and not group I.
The reason this discussion came up was because of the verb 'to rust', さびる. I guessed it to be group I, hence I thought the past tense was さびった. She corrected me, saying さびた, so I then realised the verb was group II, one of those exceptions you have to remember.
So I asked her, if I told her a new word (verb) in Japanese, would she always produce the right inflections? Surely a Japanese child would come across this problem from time to time? Anyway, she looked a little puzzled, but then again, I don't suppose she'd ever thought about it before.