I have heard that Japanese has the largest number of words of any language because every Chinese word can also be a Japanese word. Is there any truth to this statement?
Although it's true that there are a very, very large number of kanji compounds imported from Chinese to Japanese, it's not as direct as that statement. There are Chinese words that don't exist in Japanese, and many Chinese Kanji have different meanings or pronunciations, as well as occasionally being written slightly differently. These differences are particularly profound in words with grammatical significance:
- 你 (cn: nei5; jp: ni, ji, nanji) - Chinese for 'you'. Very common in Chinese, rare in Japanese (other words are used instead)
- 我 (cn: ngo5; jp: wa, ware) - Chinese for 'me'. In Japanese carries a connotation of referring to yourself as a representative of a larger group, and is therefore somewhat uncommon.
- 的 (cn: dik1; jp: teki) - Chinese possessive particle; has a function similar to の in Japanese. In Japanese, this is a suffix meaning 'the essence of'. You see this used in, eg, 攻撃的 or 積極的, but it is not used the same way as in Chinese at all.
There are also differences in usage patterns for modern inventions - eg, Chinese uses 电脑 for 'computer', but in Japanese the katakana コンピューター is more common.
As for whether there are more words in Japanese than other languages, I couldn't say. I would suspect, though, that if you looked at the set of commonly used words, it would be about the same; if you were to include classical words, loanwords, and rarely used native equivalents for loanwords, you might see a bit more than the average language.
The Chinese calligraphy came to Japan approximately 1,500~2,000 years ago, so I'd argue that that statement goes the other way: Chinese people can read many Japanese words and grasp quickly what they mean.
Chinese, on the other hand, uses many, many kanji that are not found in Japanese's ~2,000 常用漢字 joyo-kanji taught in the education system. So, I don't think it's true that Japanese people, without proper study, can read Chinese words, nor does it mean that for that reason Japanese has so many words.
You are correct in noting that Japanese does have a lot of words because various nuances can be formed by combining slightly different kanji with similar meanings. When I was learning about 状態, I was very frustrated to find that 実態, 事態, 状況, 実況, and 事情 all more-or-less translated as "circumstances" or "situation" in my dictionary at the time.
Soapbox: that's why learning kanji can be good for your vocabulary - it becomes about understanding the nuance of the kanji, not rote memorization of a bunch of words.
Not EVERY Chinese word. But lots and lots of them. China has always been the dominant culture in that area, so there are lots of Sino-Korean, Sino-Vietnamese and Sino-Japanese words. Writing was imported from China and later adapted for Japanese. When the Dutch brought over all of their science and medicine books, all of terms that didn't exist in Japanese were translated using Sino-Japanese words.
Slowly katakana English is taking over, however, meaning that there are a huge number of words with both English and Chinese counterparts. Even if Japanese doesn't have the biggest vocabulary in the world (remember diglossia in Arabic societies, languages with morphology so complicated that it denies all attempts to count words, etc.) it still is huge.
You need to know that languages will evolve over time. Parts of the Japanese language was largely influenced by classical Chinese, so a lot of Japanese words you see will make sense in Chinese and vice versa. However Japanese and Chinese are different language so even if they share similar volcabulary they are not simliar grammatically wise.
Some words in Japanese means the same thing in Chinese and Japanese. This is the case about 75% of the time. Then there are cases where Japanese words make sense in Chinese, but Chinese people tend to not use them. For example the word 上手 means to be skilled at something. If you say that in Chinese people will (probably) understand you but it's not natural because it's like saying "grand fries" in English rather than "large fries"
Then there are cases where Japanese words means something completely different in Chinese. For example 勉強 means to study in Japanese, but in Chinese it means reluctance.
This actually came up in class awhile back and our sensei (native speaker) answered roughly as follows:
A Japanese person going to China will recognize enough kanji to be able to get around and maybe get the gist of a newspaper article but since Japanese uses a limited subset of the sinographs, they will not be able to read everything they see and will also encounter problems in regards to interpenetration due to the changes since when they were first introduced. Likewise, Chinese person will recognize enough kanji that they can also get around if they visit Japan, but will encounter the same problems with interpretation and would also need to learn the hiragana and katakana.
Couple this with the differences in grammar (i.e. verb-final vs. subject-verb-object) and the meaning of a sentence can also be lost even if you have a rough idea as to what the kanji mean.