This statement is not correct - especially among American manufacturers, most bolt action rifle safeties allow the action to be cycled with the safety engaged. This is either accomplished by a 3 position safety, 2 position safety without a bolt lock, or a 2 position safety with a bolt release, in the case of the newer Brownings.

Remington 700: 2 position safety, which for the last ~30 years does not lock the bolt when on safe, such the action can be cycled while the safety is on.

Winchester 70: 3 position safety to allow the action to be cycled while the safety is on.

Winchester XPR: 2 position which does lock the bolt when safety is on.

Ruger M77 MkII and Hawkeye: 3 position safety to allow the action to be cycled while the safety is on.

Ruger American & Precision Rifles: 2 position safety which do not lock the bolt, such the action can be cycled with the safety on.

Tikka T3: 2 position which locks the bolt when the safety is on.

CZ550: most 550’s have a 3 position safety which allows the action to be cycled while the safety is on.

Savage 10/110 and variants: 3 position safety to allow the action to be cycled while the safety is on.

Savage Axis: 2 position safety which does not lock the bolt, allowing the action to be cycled while the safety is on.

Howa 1500/Weatherby Vanguard: 2 position Safety which does lock the bolt (most production, I understand some early 1500’s were 3 position safeties, but I have not encountered one personally).

Browning AB3 & X-bolt: 2 position safety plus a bolt unlock button which allows the action to be cycled with the safety on. (Old A Bolts had a 2 position safety which did lock the bolt, phased out for the new AB3 design).

T/C Compass: 3 position safety which allows the action to cycle with the safety on.

Only 3 of this dozen rifle models lock the bolt when the safety is on. Safety designs which require the shooter to disengage the safety to cycle the bolt are exceptions, not the rule.

For the OP: it does take a little consideration to own a rifle which does require the safety to be disengaged to cycle the action - especially any blind magazine model which has to cycle each round to be emptied. Awareness is critical, and you really never should be completely comfortable with the idea of administrative handling without the safety engaged.

As another point in space, however, I have very, very rarely engaged the safety of my Seekins Havak match rifle. Most of the time, my bolt handle is my safety. When walking in the dark to my blind, I have the bolt closed on an empty chamber with the striker relaxed, and my magazine loaded under the closed bolt. Only when I’m actively stalking have I engaged my safety. I’ve shot about 3,000 rounds through the rifle in the last 2 years at matches without ever engaging the safety. Just a matter of deliberate muzzle management and pensive administrative management.