Is it correct that sometimes Quality Control creates problem in achieving goals? What should we do in such cases? Can we compromise on Quality?

Yes, most of the time when Project team not collect the detail Project requirement from the project team, and approval of the Quality plan from the client or stakeholder. 

In this case once you realize that quality control become a problem imediately start to develop quality control plan and complete the approval. 

Compromising the quality will defame the company as well as out come of the project which may blacklist the company for the future project.

compromise will lead to lose the Business especially in QC systamic action and determining the root cause is approparaite way to achieve our goals.

but for QA you can compromise with clear action plan

Compromising in Quality is not the way to achieve the goals. Quality has to be maintained inorder to compete with the standards. The solution to this is only to manage the time and resourses and strategize the work based on the priority.

Yes sometime the quality causes problems in achieving certain goals . in general quality shouldn't be compromised / override at all but in certain cases the deviation occure so it should be properly discussed with quality team and engineering to find solutions.taken in considration that what ever deviations made it would not cause harm or fatality to persons or damage to equipment.

Yes it is correct that sometime quality control causes problems in achieving certain goals and that is because most time Quality is not factored in as part of the project schedule. If quality is factored in and implemented properly it will also accomplish better goals in terms of eliminating or reducing rejects, repairs, reworks etc. Quality is a key element in any project and should not be compromised. Any deviation from quality should be properly discussed with engineering and quality personnel that what ever deviations be made it would not cause harm or fatality to persons or damage to property.and assurances be made and documented for future references. Quality in any project is what helps in preserving life and property. 

Controls are made to be optimized as a part on the continuous improvement managements, therefore,  during the planning stage the should be planned to be gradually implemented across the cycle to make sure Both, required quality and final Goal are there at the same time in the end of the processes line.