Strange Sage behavior grobner bases

Question

I have the following code in Sage

R.<a, b, c, d, e> = PolynomialRing(CC, 5, order='negdeglex')
I = ideal(a^3 - 1, b^3 - 1, c^3 - 1, d^3 - 1, e^3 - 1,
          a^2 + a*b + b^2, b^2 + b*d + d^2,
          c^2 + c*d + d^2, c^2 + c*e + e^2)

I.groebner_basis()

If I execute this Sage code I get a reduced Grobner base that is not $\{1\}$. If I use order='negdegrevlex' instead of lex, the reduced Grobner base is $\{1\}$.

How is that possible? The reduced Grobner base is $1$ if and only if the system formed by those polynomials $=0$ does not have solutions, no matter what monomial ordering I use.