If OP's statement that he was at the MAD-MUC departure gate at "like 5 minutes" before boarding, e.g. 15:20, for a 15:55 flight, he is entitled to collect EC 261/2004 denied boarding compensation for EUR 250 for a Type 1 flight. IB requires that passengers be at the gate no later than T-20 and OP states that he was at the departure gate by T-35. If IB offloaded him based on incorrect information from another carrier, it is for IB to pursue the other carrier for the EUR 250. But, OP's claim is against IB as the operating carrier of the flight which denied him boarding.

In addition, IB has a duty of care to OP. If it did not supply hotel and food vouchers, OP may submit his reasonable receipts for those expenses.

This issue was addressed in non-binding guidance issued by the EC in 2016. The specific issue is the act of offloading a passenger because it is believed that he will misconnect, but where he does not actually misconnect. So long as the passenger makes it to the departure gate by the prescribed cut off, he is due compensation. If IB believes that it needs more than 20 minutes to process standbys, it is free to require passengers to be at the gate by T-30 or longer, but it does not. IB could have processed all of the standby paperwork and simply held it. Had OP not turned up, it could have boarded the standbys and avoided compensation.