To 123567
It would appear your company is correct. To remain current on your FAA license When flying FAR part 91 aircraft,FAA 61.58 would apply to your case and you require as PIC
1) within the preceding 12 calendar months complete a PIC proficiency check in an aircraft that is type certificated for more than one required pilot.
2) within 24 months complete a PIC check in the aircraft for that type you are flying