Well Frank of course the HLCRST tags are wrong. But so would be the CHGRN. The "correct" way would be against "policy" since the agencies that share 424.225 don't refer to anything like that in real life. You would need to indicate that each agency seperately is on that common frequency and it is F1 for each.
The 425.35 and 425.4 frequencies listed as Hazmat are referred to as FIREGROUND and I've never heard it referred to as HAZMAT although hazmat MAY at times have used those frequencies in an incident (but it was still referred to as fireground).
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Edit I see it listed as far back as 2003 as HAZMAT so maybe it really is.
Also I see this in the 2008 version of the RRDB:
Regional Fire Dispatch Channels
Frequency Input License Type Tone Alpha Tag Description Mode Tag
424.22500 429.22500 various RM 110.9 PL 1 Bedford/Bedford Heights/Maple Heights/Oakwood Village Dispatch FM Fire Dispatch
424.07500 429.07500 various RM 110.9 PL 2 Highland Hills/North Randall/Warrensville Heights Dispatch FM Fire Dispatch
425.27500 425.27500 various BM 131.8 PL 3 Bedford/Bedford Heights Fireground FM Fire-Tac
429.10000 429.10000 various BM 127.3 PL 4 Maple Heights Fireground FM Fire-Tac
424.10000 424.10000 various BM 127.3 PL 5 Oakwood Village Fireground FM Fire-Tac
424.12500 424.12500 various BM 127.3 PL 6 Garfield Heights Fireground FM Fire-Tac
424.22500 424.22500 various M 110.9 PL 8 Talkaround FM Fire-Talk
423.57500 428.57500 WPNV956 RM 110.9 PL 11 Garfield Heights Dispatch FM Fire Dispatch
425.40000 425.40000 various BM 123.0 PL 13 Orange Village/Woodmere Fireground FM Fire-Tac
429.12500 429.12500 various BM 123.0 PL 14 Solon Fireground FM Fire-Tac
428.35000 428.35000 various BM 123.0 PL 15 Chagrin Falls Fireground FM Fire-Tac
423.77500 428.77500 various RM 110.9 PL 16 Chagrin Falls/Orange Village/Solon/Woodmere Dispatch FM Fire Dispatch
So the Alpha tags were merely the numbers from 1 to 16. Maybe the radios are really tagged like that. I have no idea but I've never heard any reference to those numbers and I've been listening to them since they were on 46.46 MHz.