No, the semantic range of δοκέω includes both transitive and intransitive senses: the transitive sense is of subjective opinion; the intransitive sense is of appearance, i.e., how something or someone is seen or thought to be, which is the sense of the word in Mark 10:42.
Here is the relevant section of the BDAG entry:
2. to appear to one’s understanding, seem, be recognized as
a. intransitive (Hom. et al.; so mostly LXX)
β. be influential, be recognized as being something, have a reputation (cp. Sus 5; 2 Macc 1:13). οἱ δοκοῦντες (Eur., Hec. 295; Petosiris, fgm. 6 ln. 58 οἱ δοκοῦντες = the prominent dignitaries; Herodian 6, 1, 2; Jos., C. Ap. 1, 67) the influential men Gal 2:2, 6b. A fuller expr. w. the same mng., w. inf. added (X., Cyr. 7, 1, 41; Pla., Gorg. 472a, Euthd. 303c οἱ δοκοῦντες εἶναί τι; Plut. Mor. 212b δοκοῦντας εἶναί τινας; Epict., Ench. 33, 12; Herodian 4, 2, 5; Philo, Mos. 2, 241) vss. 6a, 9 (Pla., Apol. 6, 21b οἱ δοκοῦντες σοφοὶ εἶναι). WFoerster, D. δοκοῦντες in Gal 2: ZNW 36, ’38, 286–92 (against him, HGreeven, ZNW 44, ’52, 41 n. 100).—οἱ δοκοῦντες ἄρχειν those who are reputed to be rulers Mk 10:42 (cp. Plut., Arat. 1047 [43, 2] ᾧ δουλεύουσιν οἱ δοκοῦντες ἄρχειν).
From The Gospel of Mark (NIGTC; Grand Rapids: Eerdmans, 2002), page 418, by R. T. France:
[....] Jesus takes up the idea of royal privilege from the brothers' request and universalizes it with regard to ἔθνη. While ἔθνη could be used here in its widest sense (this is how authority is exercised in any nation or political unit), the plural far more often in the NT denotes the Gentiles. It is not so much, however, that Jesus wishes to acquit Jewish leaders of the sort of attitude to authority which Gentiles display (the Herod dynasty would have offered clear enough examples), but rather that if you wanted to look outside politically subject Israel to those who held real power, οἱ δοκοῦντες ἄρχειν, rather than simply οἱ ἄρχοντες does not question the reality of their rule, but rather draws attention to the fact that they are seen to rule, that their status is publicly recognized. Cf. οἱ δοκοῦντες for influential people in Gal. 2:2, 6, and with infinitive 2:9; see further G. Kittel, TDNT 2.233.