Company asks for 30 days notice in order to get accrued PTO/eligible for rehire - is it a mistake to give 2 weeks?

So I really don't like my job and would like to start my new job that I just got offered as soon as possible. I haven't gotten back to them with a start date yet and am not sure what to do but need to decide soon.

I feel like 2 weeks is sufficient/professional - however in the employee handbook (not a contract - US & at will state), it says that in order to receive accrued PTO and be eligible for rehire you have to give 30 days notice. I don't care about accrued PTO, I take my vacation/don't roll over time and am probably only giving up 3-4 days. It's the rehire thing that I'm not sure about - how likely is a future employer to ask a former employer about rehire eligibility & will my current employer admit that the only reason I'm not eligible for rehire is because I gave 2 weeks instead of 30 days notice? (Hoping to stay at new job/company a long time, but just thinking long term/worst case)

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