Where is this mentioned? Did they actually count the total number of syllables?
Yes, It is true that Rig Veda consists of 4,32,000 syllables. It is verified by Shatapatha Brahmana in 10:4:2:23
He arranged the Rik-verses into twelve thousand of Brihatîs , for of that extent are the verses created by Prajapati. At-the thirtieth arrangement they came to an end in the Paṅktis; and because it was at the thirtieth arrangement that they came to an end, there are thirty nights in the month; and because it was in the Paṅktis, therefore Prajapati is 'pankta' (fivefold). There are one hundred-and-eight hundred Paṅktis.
As you can see above, the Rik verses (verses of RigVeda) are equivalent to 12,000 Brihatis. Brihati is a Vedic meter and a Brihati meter consists of 36 syllables. Thus total no.of syllables in Rig Veda are:
Also it tells RigVeda is equivalent to 10800 Panktis. Pankti is also a vedic meter containing 40 syllables. Thus the no. of syllables in Rig Veda becomes:
Thus, there are 4,32,000 syllables in RigVeda.