I find what @droooze wrote is interesting, but also incomplete, and sorry but "90% seems like an overestimation" is the description of a feeling, not a citation of evidence.
I think that many people will agree to answer your question as, roughly, "a majority of characters used in modern Chinese are made up from recurring parts, of which typically one hints to the very broad meaning or semantic category (of which there are but a few hundred), and one other may be understood as a mnemonic for the sound (the reading) of the character, with varying degrees of accurateness, and not infrequently clustering around more than a single 'type' of syllabic setup (of these sound-indicators, one of my sources (school material, 3900 characters listed) has around 750)."
@droooze is quite right in that many characters that have been or should be characterized as containing one or more parts that hint at the character's reading are either (1) not classical and straightforward 形聲字, or (2) have lost the utility of a 'plain' 形聲字 to the modern speaker due to historical sound changes, or are (3) just too obscure or too rare to be a useful, practical (as opposed to 'originally created as') 形聲字 in an operational sense.
So no, this is definitely not an urban myth; there are many, many false assertions floating around when it comes to Chinese language and writing, but this is not one of them. To establish reliable figures, though, is quite a bit harder; let me just ask you, before you even start counting, what is it you're asking for: the number of phono-semantic compounds in the totality of all Chinese characters? or only those as used on in mainland China? in Taiwan? the proportion of phono-semantic compounds among all (repeating) occurrences in typical modern texts?
Worse, how will you go and count, say 工 gong as it appears in 貢 gong, 江 jiang, 項 xiang, 紅 hong, 扛 kang, 邛 qiong? That 邛 'is' a phono-semantic compound may indeed matter very little to people who struggle with this character's unusual structure, rare occurrence, and aberrant reading!