You are all right.
"Many" is correct in affirmative sentences such as: "There are many cars on the road" and "the library has many books." Using "many" in affirmative sentences like these, however, is not conversational. It is perfectly correct, but quite formal and literary in style.
"Many" is seen in newspaper articles, for example:
"¢ The list of these add-ons has been expanding steadily for the last decade, pushing many drivers to the point of revolt. (The NY Times)
"¢ Until the late 1980s, many aspects of life in North and South Korea were dictated by ..........competition between the two Korean states. ...(Korea Times,)
"¢ IF "MIRACLE" is to be believed, Brooks paid no attention to a week of hockey tryouts, selecting his own team and in many cases ignoring better players because ... (Los Angeles Times)
"Many" appears frequently in newspaper headlines:
"¢ Many Seniors Eager to Go Back to Driver's Ed Class (Los Angeles Times)
"¢ Two sides, many arguments in gay-marriage debate (Lowell Massachusetts Sun)
"¢ Chase for biotech billions pits city against many rivals (Portland Tribune)
As for what the experts say, here are the words of L.G. Alexander*:
"Much and many do not normally occur in the affirmative in everyday speech. Instead, we use a lot of and (informally) lots of:
I've got a lot of/ lots of time. I've got a lot of/ lots of books.
A lot of, lots of and plenty of ....are normally used in the affirmative. ....
I met a lot of/ lots of interesting people on holiday.
Don't worry. We've got plenty of time before the train leaves.
A lot of/ lots of are often considered unsuitable in formal style. Instead, we use much/many or other quantifiers such as a great deal of or a great amount o f + uncountable noun...A large number of/ A great number of + plural countable noun: A large number of/ A great number of our students are American."
Another expert, Michael Swan,** writes the following:
"In an informal style, we use much and many mostly in questions and negative clauses. They are unusual in affirmative clauses except after so, as and too; other words and expressions are used......In a formal style, much and many are not so unnatural in affirmative clauses..."
*Longman English Grammar, by L.G. Alexander. Longman. 1988
**Practical English Usage, Second Edition, by Michael Swan. Oxford University Press. 1995