The right of access to the courts is indeed but one aspect of the right to petition.
Step-by-step explanation:
When the constitution is looked into, it is revealed that the right to access to the courts is nothing but one of the aspects of the First Amendment’s right to petition the government for redress of one’s grievances. This can be easily seen as it is stated here, similar philosophy governs the approach of groups or citizens to administrative agencies which can both be seen as creatures of the legislature, and limbs of the executive, and to all the courts which are the third branch of the government.
Thus, it is more than implied that the right of petition is extended to all departments of the government including the courts. Thus, making it an aspect of the "right to petition".