I think the answer to your question is yes -- all seats reporting to the integrator are on the leadership team.
I'd go back to the beginning of the accountability chart exercise and take it from scratch. Start with sales/marketing, ops, and finance/admin and decide if any of those functions need to be split into multiple seats.
Based on your question I think you'll likely end up in one of two boats:
- Decide HR and IT belong under finance/admin
- Decide that at your company finance needs to be a distinct function. In that case you need to figure out where HR and IT belong, and I'd recommend creating a dedicated admin seat on the leadership team. From what you described, I think it's likely y'all would decide that the integrator being dual-hatted as integrator AND director of admin is the simplest, best structure for the company.
I encourage you to be disciplined about thinking STRUCTURE FIRST. Does it not make sense to put them under finance, or are you working around a limitation of someone on the team? If it's the latter, you're doing them no favors. Enter the danger and fight for the greater good.
Let me know if I can help in any way and good luck!