After several hours of experimentation, thinking and reading I came up with an answer. I have a rather crazy, but plausible assumption that the makers of HGST 7K1000 HDD were a bit lazy, and instead of implementing the disabling of head parking, they made the drive to make some activity (read something, I guess) in order to keep it active, so that the timer of inactivity never reaches a certain point, thus the drive is making activity sounds about each second. So, in other words, my guess is that it was easier for them to make a timer to create activity each second, rather than to change the timer which parks the heads.
Also there is a less crazy explanation, but still a bit strange: setting APM value to 254 or disabling the APM puts the drive into Active Idle mode, and it is supposedly normal (or designed this way) that drive is active each second when in Active Idle mode. Well, so that the drive doesn't become lazy and fall asleep on its job, I guess.
Here are some APM values that I have tested with the drive:
HEX DEC RESULT
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"01h - 7Fh ... The deepest Power Saving mode is Standby"
01 1 parked immediately or almost immediately
7F 127 not tested
"80h - BFh ... The deepest Power Saving mode is Low power Idle"
80 128 parked immediately or almost immediately
96 150 parked immediately or almost immediately
9B 155 parked immediately or almost immediately
9C 156 parked in about 3 sec after several read/write sounds
9D 157 parked in about 1 minute
9E 158 not tested
9F 159 parked in about 1 minute
A0 160 parked in about 1 minute
A1 161 parked in about 1 minute
A2 162 parked in about 1 minute
A3 163 not tested
A4 164 not tested
A5 165 parked in about 1 minute
A6 166 parked immediately or almost immediately
A7 167 parked immediately or almost immediately
A9 169 parked immediately or almost immediately
AA 170 parked immediately or almost immediately
B4 180 parked immediately or almost immediately
BE 190 parked immediately or almost immediately
BF 191 parked immediately or almost immediately
"C0h - FEh ... The deepest Power Saving mode is Active Idle"
C0 192 read/write sound approx. each second
C4 196 read/write sound approx. each second
C8 200 read/write sound approx. each second
E0 224 read/write sound approx. each second
FE 254 read/write sound approx. each second
"The advanced power management levels contain discrete bands, described in the section of Set Feature command in detail."
"When Feature register is 85h (=Disable Advanced Power Management), the deepest Power Saving mode becomes Active Idle."
I provided the quotations from the HGST Travelstar 7K1000 specification in quotes.