I had 13 years of piano lessons and was a music composition major in college, so this is near and dear to my heart
1) If the student doesn't have a piano at home, I'd suggest providing at the first lesson a paper/cardboard piano keyboard. My teacher gave us laminated paper keyboards, with regular-sized keys (~2 ft x 8" or so) which we used to "practice" in places with no piano, like in study hall or in the car on the way to a competition.
2) I'd also make up a short list of cheap keyboards and where you can get them, such as links to Amazon listings (including the price). I'm thinking the <$50 range here - nothing they'd want to keep forever, but something you can hand out to parents who don't want to spring for a piano.
3) I'd make a point of telling parents who don't already own a piano that their student will do MUCH better with a real piano or full-sized weighted keyboard at home. Parents who don't play the piano themselves might not realize that a 3/4 size unweighted keyboard (suitable for electronic music) just isn't going to compare to learning dynamics and touch on a real piano, and you don't want them to shell out a few hundred bucks on something that's not really going to be good enough.
Yes - re point #3. I'm not as high-level as you are, but am sort of intermediate+/
I was the Sunday School piano-person for a number of years - for some time it was okay, as there was a fairly old, but serviceable, acoustic piano available. (The powers-that-be had purchased an electronic piano a few years earlier, but I could have the old piano if I wanted it).
Then - suddenly they got rid of the old piano, and at the same time selected a Christmas pageant program that was fairly challenging - lots of fast tunes and staccatto, for example. Fairly quickly, I found out that practising the songs at home, and rehearsing them with the kids every Sunday just wasn't going to do it. I was working part-time at the time, and at the same time was trying to co-ordinate with the church secretary as to when I could come in to practise on the electronic piano (for example, obviously I couldn't come in during the daytime if there was a funeral in progress). But I needed to practise almost every day. The touch really was so different. Maybe a high-level pianist wouldn't have had a problem with it - but for me, they had to take what they could get...
Overall I'm just trying to get across the idea that using a piano at the teacher's place - and an electronic keyboard at home - might be doable, but not optimal. A teacher who is reluctant to take on a keyboard-student isn't necessarily a music snob - he/she might simply be acknowledging the difficulties.
And - the church eventually purchased an upright-grand to replace the electronic piano. I never had high-insight as to the decision, but I think they had a few guest-pianists who did not want to play an electronic piano.