Yes the molecules are being pulled apart due to the stronger gravity closer to the black hole. Space-time stretching may have some effect in the last millionth of a second before the object is pulled in, but the object will already have been spaghettified before that happens.

Here’s a bit of math to back that up:

a=G*M/r2

Acceleration = gravitational constant * mass / radius(distance to mass center) squared

G=6.7e-11

Earth check:

M= 6e24

r=6378000m=6.4e6m

a= 6.7e-11 * 6e24 / 6.4e6^2 = 9.8m/s^2

3 solar mass black hole:

M= 6e30

r_feet = 1000000m (your feet at 1000km away)

r_head= 1000002m (your head)

a_feet = 402,000,000 m/s^2

a_head = 401,998,392 m/s^2

Looks almost the same but your feet are being pulled away from your head at 1608m/s^2 , or 164x Earth gravity! You’re also going close to speed of light and have only a few milliseconds left to live.

Above is Newtonian math and is good enough to answer your question. Even if you’re going 99% the speed of light, spacetime dilation is only 14%:

γ = √(1 - v²/c²) — Lorentz factor

= √(1 - 0.99²) = 14%