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That second quote which states that "outflow valve on NG and MAX operate at 8.95 PSI" is incorrect. According to the Boeing 737 FCOM (page 751):

Two pressure relief valves provide safety pressure relief by limiting the differential pressure to a maximum of 9.1 psi.

Accordingly, that "limitation" table appears to be for the pressure at which the outflow valves operate and not the operational limit. Indeed according to the link you shared:

At cruise altitudes above FL370, the max differential is 8.35 PSI. which will result in a cabin altitude of 8000’ at FL410.

That second quote which states that "outflow valves on NG and MAX operate at 8.95 PSI" is incorrect. According to the Boeing 737 FCOM (page 751):

Two pressure relief valves provide safety pressure relief by limiting the differential pressure to a maximum of 9.1 psi.

Accordingly, that "limitation" table appears to be for the pressure at which the outflow valves operate and not the operational limit. Regarding the operational limit, according to the link you shared:

At cruise altitudes above FL370, the max differential is 8.35 PSI. which will result in a cabin altitude of 8000’ at FL410.

That "limitation" appears to be the pressure at which the outflow valves operate and not the operational limit. According to the link you shared:

At cruise altitudes above FL370, the max differential is 8.35 PSI. which will result in a cabin altitude of 8000’ at FL410.

That second quote which states that "outflow valve on NG and max operate at 8.95 PSI" is incorrect. According to the Boeing 737 FCOM (page 751):

Two pressure relief valves provide safety pressure relief by limiting the differential pressure to a maximum of 9.1 psi.

That second quote which states that "outflow valve on NG and MAX operate at 8.95 PSI" is incorrect. According to the Boeing 737 FCOM (page 751):

Two pressure relief valves provide safety pressure relief by limiting the differential pressure to a maximum of 9.1 psi.

Accordingly, that "limitation" table appears to be for the pressure at which the outflow valves operate and not the operational limit. Indeed according to the link you shared:

At cruise altitudes above FL370, the max differential is 8.35 PSI. which will result in a cabin altitude of 8000’ at FL410.

That "limitation" is probably the structural limit and not the operational limit. According to the link you shared:

At cruise altitudes above FL370, the max differential is 8.35 PSI. which will result in a cabin altitude of 8000’ at FL410.

That "limitation" appears to be the pressure at which the outflow valves operate and not the operational limit. According to the link you shared:

At cruise altitudes above FL370, the max differential is 8.35 PSI. which will result in a cabin altitude of 8000’ at FL410.

That second quote which states that "outflow valve on NG and max operate at 8.95 PSI" is incorrect. According to the Boeing 737 FCOM (page 751):

Two pressure relief valves provide safety pressure relief by limiting the differential pressure to a maximum of 9.1 psi.