Rejected from a Ph.D. program, but asked to fund the admitted applicant

Hello! I’m in a bit of a weird predicament and would love some advice on how to manage a situation that I have somehow found myself in.

I have applied to PhD programs after graduating with my masters and have yet to be accepted into a program. The rejections from the professors I’ve applied to work under have been very professional, yet unhelpful for understanding a mismatch in fit or areas to improve my profile. I am in the social sciences field and due to an insanely unique circumstance, am running a rather large lab at an R1 institution.

My lab is doing wonderfully despite university wide funding cuts, as I have managed to secure mid seven figures in grant funding for projects over the next four years, allowing me to retain a team of ~20 professional, graduate, and undergraduate researchers.

This previous cycle I applied for a PhD under a professor at the university I work at, as we have intersecting research interests and I will hopefully soon be positioning my lab under her as the primary PI (I am unable to be a primary PI without a doctorate degree at my institution). During the cycle I was rejected personally by the professor without an interview, which hurt, but I brushed it off.

Cut to this afternoon I received an email from this professor congratulating me on receiving another grant and she asked if her incoming PhD student could work on the project, as she has been unsuccessful in solidifying additional funding to start new project and wants to be able to supplement the PhD student cost to be on the dean’s good side.

This puts me in an awkward place because while I have flexible budget to partially cover a PhD student/pay this student hourly, but I would like to eventually be accepted into a PhD program myself and this feels like a slap to the face after being rejected.

I respect this professor a lot, but feel like this is just disrespectful and (frankly) strange to ask of someone that she rejected. Like somehow I am not ready enough to join her lab, but am ready enough to help mentor and partially fund a student for her.

Am I wrong for feeling like I shouldn’t take on a student that (I am sure deservingly) was offered the slot I applied for? Thoughts on a professional way to respond? (I had plenty of quick responses that come to mind, none professional)