I believe you were right to conclude E1cB would occur. Both of your considerations are exactly on point. The amount of ring strain is minimal -- if we think that it's OK to deprotonate to form a sp2-like carbon in the first place, then we've already decided that the added ring-strain is not a huge issue. Of course, the added conjugation and the entropic component of eliminating a hydroxide ion also help to drive the reaction forward.
A literature source that confirms our thinking is shown below, for your specific example no less, and it looks like there are many derivatives for which the elimination is observed. 
I'll go further to note that Scifinder didn't turn up any reaction results for for your alcohol product, or any similar derivatives, under equilibrium basic conditions. This suggests that elimination is actually quite likely, and that your answer key is wrong. It is however, possible to isolate the alcohol if acid-base equilibrium between the alkoxide intermediate and solvent/conjugate-acid is minimized.
Ragauskas, A. J.; Stothers, J. B. 13C magnetic resonance studies. 119. Tricyclo[126.96.36.199] and [188.8.131.52]octanones from substituted norbornenones via cyclopropanation and homoketonization. Can. J. Chem. 1985, 63 (11), 2961–2968. DOI: 10.1139/v85-491.
Smits, G.; Audic, B.; Wodrich, M. D.; Corminboeuf, C.; Cramer, N. A β-Carbon elimination strategy for convenient in situ access to cyclopentadienyl metal complexes. Chem. Sci. 2017, 8 (10), 7174–7179. DOI: 10.1039/C7SC02986A.