You're definitely confusing your quote with in house upgrade requirements. They're speaking of FO's not having an ATP and not meeting these requirements listed in FAR 61.159:

(4) 250 hours of flight time in an airplane as a pilot in command, or as second in command performing the duties of pilot in command while under the supervision of a pilot in command, or any combination thereof, which includes at least—
(i) 100 hours of cross-country flight time; and
(ii) 25 hours of night flight time.

The concern I have read about this section of the FAR's elsewhere, is that several FSDO's have recently raised issue with this section stating, "if the pilot doesn't have the priviliges to act as PIC (PIC type rating in an aircraft that requires it) they cannot act as PIC under the supervision of PIC for the purposes of this section. That would mean you could only use time as SIC in a non turbo jet aircraft and an aircraft under 12,500 lbs. gross weight, however, requiring a SIC to log time towards the ATP under this FAR.

Your company requirement for Captain upgrade is not involved. Those requirements I believe are completely at the discretion of the company. I've heard at GoJet the requirement for upgrade without any company time is 4500 TT adjusted with company time to 3500 TT. Correct me if I'm wrong. But that is one way they've kept their pilot costs so low. New guys with lots of time, one of which groups was United furloughs, upgrade quickly on the low side of the longevity scale and hopefully leave quickly. And most FO's get out before upgrade and the big pay bump either from being sick of waiting around or scared of the upgrade program that I've heard is more than a little shady.