The ad does not show on your last post.
No, it is not, because the net effect of either approach is identical. If you use billable expenses in Manager, those expenses do not appear in your P&L, but neither does the reimbursement from the customer. If you use a more traditional approach, your income will be higher by the billable expense amount, but so will your expenses. Net profit is identical.
The only income that does show on your Manager P&L from billable expenses comes if you mark up the expenses beyond what they cost. That is additional profit and shows up automatically in the Billable expenses - markup income account.
Please believe me, the methodology is completely correct from an accounting perspective. The only issue that could arise is whether it satisfies particular legal requirements or managerial policies for where entries are posted. But, as you already pointed out, there is great flexibility available under most accounting standards over how good accounting practices are applied. The guiding principle is usually that your method must accurately reflect the financial position of the organization at all times and its net income during a reporting period. The workflow of Billable Expenses in Manager does both.