I don't think you'll find claims that Korean coronal consonants are velar! This is unlike for example Mandarin Chinese's j- q- x- range [as transcribed in Hanyu Pinyin], which diachronically was a merger of a velar and an alveolar series in front of high front vowels. In standard Chinese though, this would never be realised as anything resembling the velar series k-, g-, h-. This points to one possible reason for the apparent confusion: should ㅈ, ㅊ, ㅉ range be phonologically labelled "palatal", "palato-alveolar", or even "alveolar". The "fundamental" nature of these phonemes has been under great debate, and so even the IPA symbols used to transcribe the phoneme vary widely.
Some of the basis is to do with palatalisation, introduced to students of beignner's Korean with ㅅ and ㅆ in front of Korean's high front vowel ㅣ (and of course in the iotated vowels / before the yod glide). However, palatalisation after ㅈ, ㅊ, ㅉ is way weaker than for ㅅ, ㅆ e.g. 저 and 져 are much more similar to each other than 서 and 셔 (indeed, for some speakers the former pair are pronounced the same). For some, this indicates a palatal nature to the phoneme.
Diachronically, it's actually the ㅅ, ㅆ range that changed though. In Late Middle Korean of the 17th century, palatalisation stopped being contrastive after sibilants, including ㅅ, ㅆ, ㅈ, ㅊ, ㅉ. Hence you see both 사람 and 샤람. This 2012 paper states that Korean dictionaries for French speakers published at the end of the 19th century explicitly state this fact. As English loanwords were adopted into the Korean language, both /s/ and /ʃ/ were transcribed unsystematically.
Apparently though, before back vowels /ʃ/ ended up getting a lot more iotation than before front vowels. This would seem to imply that a contrast between 셔 corresponding to English /ʃʌ/ and 서 from English /sʌ/ started to emerge (and the same for ㅜ /u/). Interestingly though, before front vowels, the vowel ㅜ is often added, e.g. 쉘 for Shell and 가쉽 for gossip - an effect of the phonological restriction in Korean.
For ㅈ, ㅊ, ㅉ this wasn't replicated, and as standard rules were laid down for Korean transcription, iotation was more or less officially disallowed. As palatalisation was not all that contrastive (and not phonological, according to this 2011 paper), it has also therefore not been consistent, and the extent and notability of the palatalisation has been debated quite a lot. Hence we see the inconsistency across different descriptions. All-in-all, I think it's just down to the field of Korean linguistics having developed and matured later than for English or French.
For a phonetic account, a 2004 study using stroboscopic-cine MRI from Phonetica says it's an alveolar place of articulation with a laminal tongue shape. A relatively detailed "user's" account of the articulation is found in the 2012 book The Sounds of Korean on p.77.
