It is true.

However, when we use an adjective in positive, and do not specify other degree of magnitude, 很 is added as a standard.

很 is almost used as regularly as 是. It's usually used when describing the subject with an adjective.

很 is necessary here (in a positive statement with an adjective) because of grammar.

When we describe a noun using an adjective (e.g. the cat is mean) we cannot use 是 to connect the two, but instead use 很。It then doesn't translate as "very" anymore, it's just a grammatical thing.