My company uses concur, and they pay hotel bills directly. I make my own bookings but discussions with my cow-orkers indicate that they do get points on those stays. Sometimes the booking gets screwed up and the points don't post correctly but when they call in they get fixed promptly. I would guess there's something more to it than just whose card gets charged that determines if the stay is eligible for points or not.
Let me give it a shot. First, here is the official terms and conditions:
Point or elite night credit accrual is limited to individual travel and the room must be paid for individually by the Member or direct billed to the party responsible for paying the bill. If the room is master-billed, the charges are not eligible for Points or elite night credits.
If the room is paid for by third party, the person staying can get credit so long as it is not part of a master billing. An example of what would be a master bill would be something like a business' annual meeting where the hotel sends the company a bill for all the guest rooms, conference rooms, meals and parking. An example of what would not be a master bill is where the company is sent an individual bill for a specific guest's stay and pays the bill directly. An example of that might be where a company is going to pay for someone to come in for an interview and does not want to have to reimburse the applicant so the folio is sent to the employer or a third party's cc is on file with an affidavit allowing the charge. In that case, the applicant can usually get credit. Another example I've experienced is when an airline has paid for my room because they bounced me from a flight so I was the only impacted passenger I did get credit because my room was billed individually (AirTran). When my entire flight got canceled once and they put 100+ people up, the room was part of a master billing and I did not get credit (Delta), and when Turkish Airlines put me up at a CY in Istanbul because my layover was long I did not get credit, either.
My understanding is an employer can have Concur set for any and every type of billing from all employee paid to all master billing and everything in between. And I've been to annual meetings and conventions where everyone pays for his/her own room and gets reimbursed from the same employer just so each person gets his/her own points.